Talk:Quantum state

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"Quantum System" is undefined

The "quantum state" is defined in terms of the "quantum system", but when you follow that link, it takes you to the "Quantum Mechanics" article, which does not define "quantum system".

201.215.210.189 (talk) 21:59, 13 February 2011 (UTC)

Unintelligible

What is the point of writing an article like this? What is the target audience? Possibly only the person(s) who wrote it and a few others. It needs to be carefully rewritten bearing in mind always how the reader might be struggling. I have a 1st degree in Maths and I am spending ages just trying to decipher the wording to get to the meaning behind it. Ambiguous, careless, unclear, even illogical. Hopeless. —Preceding unsigned comment added by 88.5.175.129 (talk) 00:53, 20 January 2011 (UTC)

too technical

The page is nice but it's a bit too technical for non-physics (like me!). Can it be rewritten with more user-friendliness, without perhaps sacrificing completeness?

It would really be nice to see some more on what quantumphysical characteristics of particles define their quantum states.

Technical point: The description of the quantum state as formal and non-physical, as against 'real' measurements, is highly debatable. In many accounts of quantum measurement the quantum state (density matrix) is the _only_ physical reality, the results of a measurement also being expressed in terms of a quantum state. Since everything in the Universe is quantum, including the measuring devices, the idea that the result of a measurement is somehow more 'real' can only be a shorthand for the particular type of quantum state which is produced by interactions with a measuring device and the environment.

The page as it stands gives only an old-fashioned Copenhagen-like account of measurement, which by itself is incomplete and unsatisfactory since it doesn't describe what constitutes a measurement and how the system interacts with what's measuring it.

Unfortunately quantum mechanics is the sort of subject where there is no simpler statement of meaning. Quantum states are mathematical formalities which are manipulated using (more) mathematics to gain information on real-world properties. They are not visualisable phenomena in themselves. As has been said, the reality of quantum mechanics is hotly debated and I don't think anyone has yet come up with a satisfactory answer. It's worth noting that 'quantum mechanics' in itself is not a complete theory; it works best when extended with Quantum Field Theory, which makes a little more sense though is even more complicated. 81.156.75.42 11:44, 2 April 2007 (UTC)

Uncertainty principle

I'm no expert but I think this sentance "Doing this, we determine the initial position q and the initial momentum[1] p" seems to contradict the heisenberg uncertainty principle, that we cannot know the position AND momentum at the same time. —The preceding unsigned comment was added by 138.251.252.7 (talk) 23:22, 12 May 2007 (UTC).

Huh?!

I dont know a quark about this theme, but I will like to. I think that after this sentence: "A quantum state is any possible state in which a quantum mechanical system can be.", should come a brief explanation about of those possible states or at least some examples. And then the rest: "A fully specified quantum state can be described by a state vector, a wavefunction, or a complete set of quantum numbers for a specific system."

I agree about the first sentence mentioned above: the opening sentence of the article seems tautologous, and it doesn't become clearer until one reaches the Superposition and Pure/Mixed sections.

Seems tautologous? I've seen billiard balls that weren't as circular as that sentence! "In quantum mechanics, a quantum state is any possible state in which a quantum mechanical system can be." Well, that clears it right up. Gee, thanks. And I suppose the science of physics is the branch of science that deals with physics.

I agree that this article is unclear. It certainly didn't give me the information I was looking for. Fresheneesz 02:28, 22 May 2006 (UTC)

This article is the most impenetrable I've ever seen on Wikipedia, and that's saying something.

The tautology in the opening sentence here is unfortunate, but mostly unavoidable. If any Wikipedian can come up with a precise, friendly definition of a quantum state, then I'd give them a hearty slap on the back, because the fact is that no such definition exists. Quantum mechanics is somewhat self-referential in that respect. A state is how something is. Two states are the same if there is no way to tell them apart via a measurement. That's about the sum of it. Between this and the fuzziness of the definition of 'measurement', you'll find that circular logic is just about unavoidable when dealing with the fundamentals of QM.

Mathematically, a quantum state is a unit vector in a complex Hilbert space. The question is: What do the elements of that vector represent? Each element has two parts (1) a description of a the state of a measurable parameter of the system and (2) an amplitude. There is little question about what the amplitude means. Its norm is the probability of finding the parameter in the described state when a device for measuring that parameter is used to make a measurement. Often, the measurable parameter is simply a classically defined particle attribute, such as its position or spin, but it can also be defined at a more grossly sensible level as, e.g., a detection recognized by photon detector number 3. My experience is limited here, inasmuch as I am not even a physicist, let alone a quantum physicist, but I think a definition along these lines could be improved by an expert who would take into account problems posed by conjugate pairs of attributes and vectors that define both continuous attributes (e.g., position) and discrete attributes (e.g. spin).

Heimdall2 (talk) 22:34, 13 July 2009 (UTC)

Antimatter

Could someone who knows enough about it please add something about the quantum state necessary for antimatter and matter to annihilate with each other when they come into contact with one another? Thanks!

scienceman 23:18, 23 March 2006 (UTC)

IMHO that would be misplaced in this context, this page being a general description of states in quantum theory. Matter / antimatter states are a specific feature of quantum field theory (i.e. quantum theory + special relativity), and annihilation processes are in fact a question of scattering theory (or of the interaction of the system, if you like), not of the quantum state. See Antiparticle and PCT Theorem.

--B. Wolterding 12:00, 30 April 2007 (UTC)

Merge with excited state, and Energy level

I think it would be a good idea to merge Energy level and excited state with this page. They are all very related concepts, and excited state in particular is a trivial subset of the quantum states - and could easily be a simple section on this page. Any comments? Fresheneesz 02:35, 22 May 2006 (UTC)

I might support making stationary state, energy level, excited state and ground state into the same article. (I think if you want to suggest any of those mergers, then you have to do all of them). On the other hand, I think it's too much to merge it into this article (quantum state). Rather, this article should have a section on stationary states, with a {{main|stationary state}} tag linking to the big article about eigenstates of the hamiltonian (strictly speaking, I think an energy level is an eigenvalue, not an eigenstate, so it's not a quantum state, right? so the proper article to link to is stationary state, not energy level). -lethe ^{talk +} 02:45, 22 May 2006 (UTC)

Sounds like a good plan. I don't know when i'd get to doing that tho. I'll try to start a merge of some of those soon. Fresheneesz 06:00, 22 May 2006 (UTC)

Looking at the articles, I've come to the opinion that energy level should not be merged. There is simply too much to say about calculation of energy levels. So I guess I'm left considering a merger of stationary state, excited state, and ground state. -lethe ^{talk +} 15:50, 22 May 2006 (UTC)

I merged ground level and stationary state, but I don't think there's a good way of merging excited state as well - unless its merged here (quantum state). I don't see a problem with merging those here, its not that much info. And, they all fall under the category of quantum states. Fresheneesz 02:27, 23 May 2006 (UTC)

Please DO NOT merge energy level with quantum state. A quantum state is a distinct entitity, with a number of observables, only one of which is it's (eigen) energy. The energy level entry needs improvement, and should state something like the following: "Multiple states may have the same value of the energy, in which case they are called degenerate states." For example, there are four distinct n=2 states in hydrogen (one 2s, three 2p). In the absence of any external field, they are precisely degenerate. They form an energy level. However, they are quite clearly not the same quantum state, as they result in different values for other observables, such as the electron's angular momentum, or it's projection. Thus, and energy level can contain many quantum states and it is not appropriate to merge this topic with the quantum state topic. I propose we remove the suggestion to merge the energy level article with this one. Az7997 19:08, 2 June 2006 (UTC)

oppose merger - Quantum state is a specific universe of physics theory. Excited states exist in classical mechanics and thermodynamics. A merger would be nonsense. Anlace 03:07, 18 September 2006 (UTC)

• Oppose merger of Quantum state and Energy level. Quantum state is a somewhat theoretical article on Quantum mechanics, particularly electron quantum states. I have recently expanded the Energy level article to cover molecular orbitals, vibrational and rotational energy levels in molecules, and energy level transitions between electronic, vibrational, and rotational energy levels, and photon emission and absorption in a practical sort of way, as opposed to a rather theoretical physics discussion (well - matter of opinion). Upon briefly reviewing both articles, I think Quantum state and Energy level are now quite different articles, neither one being very short, and both covering their own material in their own sort of way without that much overlap. However, Ground state and Excited state are rather short and could be merged into Energy level, especially since Energy level pretty much covers their most important material anyway. I think I'll make a note of this potential merger of Ground state and Excited state into Energy level on the Talk:Energy level page also. H Padleckas (talk) 05:31, 10 January 2011 (UTC)

Keep'em seperate

I'm not a total science person, but I know enough to know that they should probably be kept seperate. I think the beauty of wikipedia is to have as much detail as possible on different pages. As long as the topics are well-linked, the info is accessable.

65.211.131.10 21:24, 9 June 2006 (UTC)

oppose merger quantum state is a specific universe of physics theory. excited states exist in classical mechanics and thermosdynamics. a merger would be nonsense Anlace 03:06, 18 September 2006 (UTC)

Background info added

I added a link to NASA to the excited state page to help make the information a little more user-friendly. That might also be a good base reference for anyone who wanted to make the wikipage more basic/complete.

Not clear

"All experimental predictions (?) are based on the quantum state of the system and the quantum operations acting on the state. ": it is not clear to me.Sangak 19:41, 5 February 2007 (UTC)

new first paragraph -

At the outset it could be made clear that this is a mathematical description using statistics to describe experimental results. It should not be confused with being an actual representation of anything real. 220.101.73.119 23:40, 10 March 2007 (UTC)bluehigh

There are a lot of other unclear places. For example, what is the status of an eigenstate. Why should they exist ? Are they only mathematical objects or there is a fundamental low of the nature that guarantee their existence ?

Conceptual introduction

It has been remarked that this article was very technical. I have tried to fix this by adding a "conceptual description" that includes only minimal technicalities. The drawback is that the article is now rather lengthy.

Maybe there are still some aspects missing (due to brevity). Maybe parts of that description might be moved to State (physics). Comments are appreciated.

Supposing that no one protests, I would also like to update the summary and part of the second section, which are now a bit out-of-sync with the new (first) one. I would also add some details to the last section "mathematical description"; just the reference to "GNS construction" is not quite what one would expect.

In my opinion, the "concept" template can be removed now. Any opinions? --B. Wolterding 15:41, 6 May 2007 (UTC)

i think the section you added is fine, although it could be more succinct, and gives sufficient reason to remove the "context" template, the problem with the intro pointed out by Steve below notwithstanding. the neglected state of the "mathematical formulation" section can probably be blamed on me. if it does get fleshed out, perhaps a good remark to include would be that, given an algebra of classical or quantum observables, a physical state is a positive linear functional on the algebra. Mct mht 05:47, 25 October 2007 (UTC)

The conceptual introduction is excellent. It provides an explanation of quantum states in relation to classical mechanics in a way that's very accessible to a layman (like myself). In fact, it's one of the best explanations of this type I've seen. And it's even structured properly: general aspects first, technical aspects later. It's extremely frustrating to see mathematical or physics wiki articles that begin with technical jargon. Well done. RabidDeity (talk) 01:23, 11 April 2008 (UTC)

Inaccuracy in intro?

The intro states, "For example, in the case of a single particle in a one dimensional box, the state of a particle can be defined by a single quantum number related to the energy of this particle." A general quantum state is a superposition of every energy eigenstates, each with a potentially different complex coefficient, so the state characterized only by an infinite sequence of complex numbers, right? Or am I misunderstanding how the term "quantum state" is being used? --Steve 21:40, 24 October 2007 (UTC)

i think you're right. the article agrees with you, except in the intro. it's not clear to me what the quoted statement is saying. in fact, it's not clear at all what most of the introduction is saying. for instance, we have "A fully specified quantum state can be described by...a complete set of quantum numbers...". what does that mean? Mct mht 00:28, 25 October 2007 (UTC)

I agree, the introduction needs to be rewritten. In general the link between the physical concepts and the mathematical objects is not really well explained. I really need to add that "Mathematical formulation" section...

Now for the quantum numbers: What physicists mean here is a label for a basis in the Hilbert space. The link is as follows: Pure states correspond (more or less) to vectors in the Hilbert space. It usually suffices to consider a basis (often, the basis of eigenstates of the energy operator). Mathematicians would write the basis as something like $\{\psi _{j}\}$ with say an integer index $j$. Physicists just write $|j>$ instead of $\psi _{j}$ and call $j$ a "quantum number". If the energy operator does not have degenerate eigenvalues, you can take its eigenvalues as the label $j$ ("the energy as a quantum number"). If it does have degenerate eigenvalues, you need to add other labels to distinguish the basis vectors (example: the eigenvalues of the angular momentum operator), that leaves you with a "set of quantum numbers".

In short, the intro needs a rewrite and I didn't do that when I found the article and added the "conceptual introduction"... But maybe I should. --B. Wolterding 09:21, 25 October 2007 (UTC)

statements such as

the quantum state of a system is a set of numbers that fully describe a quantum system. ...These numbers are called the quantum numbers of the system.

and

A fully specified quantum state can be described by ... a complete set of quantum numbers for a specific system.

is really bad, imprecise, and highly misleading language. i'd be surprised if that's common physicist's jargon. if it is, i suggest it be not used in the article. Mct mht 02:25, 28 October 2007 (UTC)

I rewrote the lead paragraph now. Comments are appreciated. --B. Wolterding (talk) 17:08, 17 November 2007 (UTC)

I think it's on the right track, but I wish there was a better first summary sentence than "a complete description of the parameters of the experiment". When I read this I think, "okay, a quantum state is how much liquid helium I put into the dewar, what brand of monochrometer I'm using, etc.".

I'm thinking, maybe something along the lines of,

The quantum state of a system is a set of numbers that fully describes the quantum system. One typically imagines some experimental apparatus and procedure which "prepares" this quantum state. Quantum states can be statistically mixed, corresponding to a experiment involving a random change of the parameters. States obtained in this way are called mixed states, as opposed to pure states which cannot be described as a mixture of others. When performing a certain measurement on a quantum state, the result is in general described by a probability distribution, and the form that this distribution takes is completely determined by the quantum state and the observable describing the measurement. However, unlike in classical mechanics, even the measurement of pure quantum states is only determined probabilistically. This reflects a core difference between classical and quantum physics.

(The first two sentences, I wrote into this article.) Comments? --Steve (talk) 18:01, 20 November 2007 (UTC)

I think this is an improvement on what is there - I like it. I particularly like the statement about the apparatus and procedure that prepares the state. PhySusie (talk) 18:19, 20 November 2007 (UTC)

• Fine for me in principle, but I disagree with the "set of numbers". (Describing e.g. an $L^{2}$ function as a "set of numbers" seems like stressing the picture too far.) How about this one:

In quantum physics, the quantum state of a system is a mathematical object that fully describes the quantum system. One typically imagines some experimental apparatus and procedure which "prepares" this quantum state; the mathematical object then reflects the setup of the apparatus. (...)

Also, I suggest "measurement of pure quantum states" -> "measurement results in pure quantum states" in the last sentence. --B. Wolterding (talk) 18:28, 20 November 2007 (UTC)

I like the "mathematical object that fully describes the quantum system" part - much nicer. The second recommendation though doesn't work grammatically. PhySusie (talk) 18:46, 20 November 2007 (UTC)

Well, what I wanted to point out is just that not the measurements are probabilistic, but the measurement results. (A very minor point of course.) --B. Wolterding (talk) 15:40, 21 November 2007 (UTC)

Ah! Now I see what you meant - I was reading the word 'results' as a verb and you were using it as a noun - lol - sorry. Maybe use 'the results of measurements of pure quantum states' instead - and its not a minor point, that is important to keep clear. Go for it! PhySusie (talk) 17:29, 21 November 2007 (UTC)

"In quantum physics, a quantum state is a mathematical object that fully describes a Quantum system" Ok, I am a lay person and am not sure if I am understanding this correctly. Is a quantum state a mathematical object or a condition of nature? —Preceding unsigned comment added by Tunepoet (talk • contribs) 05:05, 9 May 2009 (UTC)

Accessible

I just read about 80% of this article. It is understandable and accessible. To those who worked to make this article accessible and understandable - Good job! Ti-30X (talk) 04:58, 1 September 2009 (UTC)

I agree. The article is very helpful for someone like myself who is more familiar with statistics and linear algebra than physics. Explaining often mentioned QS concepts in a language that I understand (v. the usual hand-waving with often misleading analogies and examples) gives me a good starting point for further study. Thanks. —Preceding unsigned comment added by 76.88.4.187 (talk) 15:58, 12 February 2011 (UTC)

Quantum system

The link for "Quantum system" actually delivers the user to "physical system," and that article does not say anything about a quantum system as distinguished from a classical system. P0M (talk) 20:03, 16 June 2011 (UTC)

Basis state

Basis state is red. It's probably more appropriate to explain it here than at basis (linear algebra). Briefly, the reader needs to know why a basis is needed (states are vectors), that the basis states compose non-basis states through linear combination, & the bra-ket notation for composing a state from the basis states. If my thinking's solid, the formula from particle number operator would work for all, with the ν parameter unnecessary. ᛭ LokiClock (talk) 13:54, 22 September 2011 (UTC)

"Clarification needed"...

• "Consider an experiment with a (non-quantum) particle of mass m = 1 that moves freely, and without friction, in one spatial direction. We put the particle at initial position q and start the experiment at time t = 0 by pushing the particle with some speed and in some direction. Doing this, we determine the initial momentum p of the particle. These initial conditions are what characterizes the state σ of the system, formally denoted as

$\sigma =(p,q)$

We say that we prepare the state of the system by fixing its initial conditions." <-- right - it seems that q is position and p is momentum, and these are continuous variables which can take any values, and σ is just the state, the 2-tuple containing p and q.

• "At a later time t > 0, we conduct measurements on the particle. The measurements we can perform on this simple system are essentially its position Q(t) at time t, its momentum P(t), and combinations of these. Here P(t) and Q(t) refer to the measurable quantities (observables) of the system as such, not the specific results they produce in a certain run of the experiment." <-- This is confusing. What are P and Q? Based in this description they are simply labels for position and momentum (at time t?) and not the continuous variables which are measured in an experiment, but then it says "measurable (observables) of the system", why?
• "However, knowing the state σ of the system, we can compute the value of the observables in the specific state, i.e. the results that our measurements will produce, depending on p and q." <-- Now this returns to p and q.

Does anyone know what the section tries to say?-- F = q(E + v × B) 17:20, 21 January 2012 (UTC)

There are a couple of ambiguities earlier in this article. I think they are simply English-writing ambiguities. If I fixed them wrong, then some deeper examination needs to be done.

As for

Here P(t) and Q(t) refer to the measurable quantities (observables) of the system as such, not the specific results they produce in a certain run of the experiment.

it appears to me that the intent of the writer was to speak from the standpoint of classical physics and maintain that there are real facts about the universe that include P at time t and Q at time t that (measurable =) can be measured—assuming that we do things right. Getting some reasonable approximation of "right" involves "specific results" in many "run[s] of the experiment."

At this point I have one foot on the dock and the other foot on the rowboat. Assuming that the above part is correct, then the rest of it would mean that future measurements can be predicted. But in that case it would seem to me that the sentence should have "'given as future observations of p and q", and not "depending on future observations of p and q.

I'm afraid the above guesswork is not very useful. It might result in correct sentences but obscure the intended, and more salient, meaning originally intended.P0M (talk) 18:43, 21 January 2012 (UTC)

I still don't understand what you mean by P and Q. So we are both confused? This should be notified at the wikiproject page which has been done now.-- F = q(E + v × B) 21:39, 21 January 2012 (UTC)

I personally do not mean anything by the two letters. However, I am guessing that they were intended to represent the real facts about the thing being measured. In other words, I am guessing that those capital letters refer to the realities that experimenters are trying to measure. But whoever wrote the sentences in question should be the one to help straighten things out.P0M (talk) 22:10, 21 January 2012 (UTC)

Yes - that user should, but what is the chance (excuse probability/QM pun) of that occurring? All we can do is wait for someone from the wikiproject talk page to reply...-- F = q(E + v × B) 22:21, 21 January 2012 (UTC)

See http://en.wikipedia.org/w/index.php?title=Quantum_state&direction=next&oldid=128407213

This formulation has been around for quite some time. If it doesn't mean anything useful to anybody now involved, maybe the best thing to do is to delete it.

The statement was written in 2007 and the editor who wrote it has not been active since 2010. No use waiting...P0M (talk) 23:18, 21 January 2012 (UTC)

You raise a good point, and may be correct about deleting. Shall we?...-- F = q(E + v × B) 00:25, 22 January 2012 (UTC)

They appear to use confusing notation in the example, it seems they should have used P(0) and Q(0) for the initial state. They should have then explained that P(t) and Q(t) were functions for how these values change in time. In this particular case P(t) is the function for the momentum whilst Q(t) is the function of position in a classical treatment. Classically, the initial state, i.e the values of P(0) and Q(0) determines the future evolution of the system exactly. The line that reads not the specific results they produce in a certain run of the experiment. is incorrect; since the example is within classical physics P(t) and Q(t) do represent the specific results they produce in a certain run of the experiment presuming experimental error is eliminated. IRWolfie- (talk) 16:07, 22 January 2012 (UTC)

So sorry not to reply... I’ve been caught up in other pages and not even monitored this one. What you say is clear and correct. It seems the consensus is just to re-write the first couple of paragraphs in the first couple of sections? Trouble is I only know some, not all, of the real meanings and implications of quantum states inside-out (yet)... else it would have been done by now...-- F = q(E + v × B) 00:41, 24 January 2012 (UTC)

From what I have read, written by some of the greats in the field, I am not sure that there is a single understanding of what a "state" is. So I think you need not be too critical of your own writing. If we can get beyond the state of having something that "isn't even wrong," then we can hope to make progress.

It seems to me that some people regard the state as something that is really there and that experimenters are trying to describe accurately, but that for other the state is the abstraction that has some tentative relationship to reality, i.e., the state is a mathematical model or a "convenient fiction" and nothing more. I believe this difference in opinion (or interpretation) must apply to the whole article and not just to this one small part of it.P0M (talk) 01:16, 24 January 2012 (UTC)

An alternative to re-writing the paragraph would be to mention the classical analogue as required in the prose of the section that follows it. I wouldn't mind giving it a stab. IRWolfie- (talk) 11:33, 24 January 2012 (UTC)

Sounds good to me.P0M (talk) 15:13, 24 January 2012 (UTC)

I gave the section a bit of a rewrite to clarify some things that seemed wrong or confusing. I removed references to the previous section, the section "The state of a physical system" could be removed as it can be accessed in the history. I will try, later (I'm in work), do some more edits on the section "Quantum states" to sum up any relevant points from the section "the state of a physical system". IRWolfie- (talk) 10:33, 25 January 2012 (UTC)

Good effort! Though it may be better to change the description slightly along these lines: rather than say "we push on the particle with speed", its more accurate to say "an external agent moves the particle with a definite momentum (and hence speed)", since there is a more direct statement to momentum and is more formal. Then again, its supposed to be explained as plainly as possible for the average reader. Thanks for your help =) -- F = q(E + v × B) 22:18, 25 January 2012 (UTC)

So you deleted it... That’s probably the best move actually, but it did provide analogy with classical mechanics and climaxing with statistical mechanics, to some extent, and statistical mechanics is a good stepping stone towards QM. Anyway the problem of clarification is now over; "if in doubt: leave it out". -- F = q(E + v × B) 20:20, 26 January 2012 (UTC)

I'm still planning to go over it again and provide some form of analogy but I think in the interim it is best left out. IRWolfie- (talk) 11:58, 27 January 2012 (UTC)

A question about the lead section

Consider a system with just 1 hydrogen atom. The wave function for the electron only requires 3 quantum numbers $\{n,\ell ,m_{\ell }\}$. This wave function can give hydrogen's probability density in position space and momentum space. So, what other information about the position or momentum of the electron are not specified?--LaoChen (talk)06:17, 31 October 2012 (UTC)

Those three quantum numbers do not say what the electron's spin is. --Steve (talk) 13:22, 31 October 2012 (UTC)

Note that the talk page is for making improvements to the article. For questions about the physics, try the reference desk. IRWolfie- (talk) 14:40, 31 October 2012 (UTC)

Thanks for your reply. However, I think the spin is inherent in the specification of been an electron. Is there an electron with spin 3/2? I think we should delete the first paragraph's last phrase about the position or momentum of the electron. I'll send the question to the reference desk to make sure the lead section shows the accurate physics. --LaoChen (talk)04:50, 1 November 2012 (UTC)

Electrons have spin 1/2. I'm not sure what issue with the first paragraph that you are referring to. If you want more opinions related to the article try wikiproject physics. IRWolfie- (talk) 14:33, 1 November 2012 (UTC)

I propose to change the first paragraph of the lead section to as follows:

In quantum physics, quantum state refers to the state of a quantum system. It's specified by a state vector of a Hilbert space. The state vector theoretically contains all the interested information the most information possible about the quantum system. For example, the state vector of an electron within a hydrogen atom is given by its four quantum numbers $\{n,\ell ,m_{\ell },m_{s}\}$, and this specifies four properties (The principal quantum number: n, The azimuthal quantum number: ℓ, The magnetic quantum number: mℓ,The spin projection quantum number: ms ).

The changed statements are supported by referenced textbook. If nobody disagrees, I shall proceed to edit with the above modification.--LaoChen (talk)18:01, 1 November 2012 (UTC)

I would strongly suggest keeping the discussion in the lead to the non-spin quantum numbers, and explicitly mention that spin is being neglected there. Most texts introduce quantum states this way, and even for hydrogen the spin states are more complicated than you would want to go into in the lead. They could, however, be mentioned in full in the subsequent section on spin states. (To really treat it in full, you also need to specify the spin state for both the electron and the proton, rather than just the total spin). a13ean (talk) 15:44, 2 November 2012 (UTC)

A13ean, you are saying that the spin of the electron may be entangled with the spin of the proton. Well, that's true. But the position of the electron is also entangled with the position of the proton. (The proton is not infinitely heavy.) At a greater level of accuracy, both the position and spin of the electron are entangled with each other (spin-orbit coupling), and with the photon field (cf spontaneous emission) :-) So I am not convinced that mentioning the spin in that sentence is more of an oversimplification than mentioning the position in that sentence. I do think that spin should be mentioned in the first few sentences, as the main difference between the technical terms "quantum state" and "orbital" is that the former but not the latter considers spin.

LaoChen, I think what you wrote is pretty good, except that it implies that all possible states are specified by the four quantum numbers. But in reality, it is quite possible for an electron to be in a superposition of 1s and 3p or whatever. :-) (I know that this problem was already in the article for a long time, it's not your fault.) This could be fixed with a small wording change. --Steve (talk) 22:46, 2 November 2012 (UTC)

Just word that it's for an eigenstate. IRWolfie- (talk) 23:28, 2 November 2012 (UTC)

If we give an example in the first paragraph, it ought to be a simple and well-thought-of example, otherwise, we would spend a lot of time covering all the strange cases. Thus, I propose to change the first paragraph of the lead section to as follows:

In quantum physics, quantum state refers to the state of a quantum system. It's specified by a state vector of a Hilbert space. The state vector theoretically contains the most information possible about the quantum system. For example, when dealing with the energy spectrum of the electron in a hydrogen atom, the relevant state vector is given by the principal quantum number $\{n\}$. For a more complicated case, consider Bohm formulation of EPR experiment, where the state vector $\left|\psi \right\rangle ={\frac {1}{\sqrt {2}}}{\bigg (}\left|\uparrow \downarrow \right\rangle -\left|\downarrow \uparrow \right\rangle {\bigg )}$ involves superposition of joint spin states for 2 different particles.

There are chiefly two very different interpretations when dealing with the concept of state vector. One is the statistical interpretation advocated by Albert Einstein. It theorizes that quantum state tries to provide as much as possible the statistical properties of an ensemble of similarly prepared systems. However, sometimes, it can not give a complete description of the system. The other interpretation is exemplified by the Copenhagen interpretation and championed by eminent physicists Erwin Schrödinger and Niels Bohr, among others. It proclaims that quantum state can completely describe the quantum system under examination.

Please comment. Hopefully, the article's lead section can be improved further, thanks!--LaoChen (talk)06:23, 3 November 2012

Each vector in one particular basis for the bound states of one proton and one electron (if one ignores the location and motion of their center of mass) can be associated with a five-tuple:

• the principal quantum number
• the azimuthal quantum number
• the magnetic quantum number
• the electron's spin quantum number, and
• the proton's spin quantum number.

How does one extend this to a complete basis which would include unbound states? JRSpriggs (talk) 07:08, 3 November 2012 (UTC)

These seem like very interesting content. Perhaps we can have a section just for the bound states and unbound states of the hydrogen atom. Hopefully, someone familiar with atomic physics can provide more content.--LaoChen (talk)19:22, 7 November 2012 (UTC)

If everyone agrees to the proposed changes, let me give it a try then.--LaoChen (talk)05:26, 14 November 2012 (UTC)

Minor formatting problem

Near the beginning there are two sentences beginning with a bold-face A. The text shouldn't take this form, but I can't see where the problem lies. "A pure state and A mixed state..." It looks like something might not have been terminated earlier. Strange behavior. Can anyone fix it?P0M (talk) 04:49, 15 November 2012 (UTC)

I have tried to make the lead section clearer and more consistent in physics. Since the lead section tries to run over a lot of ground for the abstract concept which is a lot different from the classical concept, there may still be a few fine points that I have missed. I am not sure which two sentences are giving you problems. It would be nice if they can be fixed.--LaoChen (talk)07:04, 15 November 2012 (UTC)

Strong implicit interpretation assumptions

The validity of statements like "even pure states show statistical behaviour" depends very much on the assumed interpretation of the "measurement problem" in quantum mechanics. Statements of this kind can only be justified once the framework of ensemble interpretation (or similar) is adopted. A typical textbook which follows this interpretation is "Modern Quantum Mechanics" by Sakurai (who even talks about such strange things as "pure ensembles"). Unfortunately, from the point of view of people who believe that the state can contain complete information about the system (and solve the "measurement problem" by other means, e.g., decoherence), this statement is very wrong. It is the measurement setups which "show statistical behavior", not states.

I suggest that the article should significantly expand on the concept of "state" in a sense that it is a description of a system which disregards previous history of the system, perhaps making a connection to Markov processes. — Preceding unsigned comment added by 129.118.41.225 (talk) 00:10, 22 January 2013 (UTC)

"the above example is pure"? no!

Maybe 'the above example' is ill defined but the given wave function, a bell basis state, is maximally mixed and thus the opposite of pure. The state vector of a hydrogen energy spectrum is pure though, so maybe that is what is referred to. (by Physics Grad Stud) 145.107.69.79 (talk) 12:57, 19 August 2013 (UTC)

"Mixed states" and "entangled states" are not the same notions. A Bell state is pure and maximally entangled. Mct mht (talk) 09:03, 20 August 2013 (UTC)

Thanks! I really need to get my definitions straight. 145.107.68.226 (talk) 14:28, 21 August 2013 (UTC)

wave functions are also representations of quantum states

The lead says that the quantum state has to be a vector, but as far as I'm aware that's just one way to encode a quantum state. Wave functions are also used to represent quantum states. Am I wrong about this? --Nanite (talk) 10:04, 6 December 2013 (UTC)

Wave functions are vectors in a Hilbert space. --Bob K31416 (talk) 17:07, 23 December 2013 (UTC)

Do eigenstates exist for every observable?

I’d wonder if Mr. L. E. Ballentine really said that “for every observable there are states that determine its value exactly” (outside a finite-dimensional context) and had his textbook printed on paper afterwards. If he did, then he should be disqualified because only an operator with a non-empty point spectrum has eigenvectors. Incnis Mrsi (talk) 11:58, 7 January 2014 (UTC)

It's unclear to me what's wrong with the statement, since it seems equivalent to how observables are defined. a13ean (talk) 18:43, 7 January 2014 (UTC)

Lolwut? Consider a particle on the line, or on the circle, or in a box. Which quantum state “determines exactly” the value of the position operator? Incnis Mrsi (talk) 21:42, 7 January 2014 (UTC)

Perhaps you didn't read the statement carefully enough? I think you know how to project a Dirac function on the base kets (but if not you can read about it here). Also, let's remember the talk page is for discussing the content of the article, not chatting on the topic. If you think there's a fundamental flaw in a highly cited RMP review, why don't you find a reliable source that disagrees with the above (rather weakly phrased imho) statement? a13ean (talk) 16:33, 9 January 2014 (UTC)

So what? James Cresser with his δ intervals virtually explicates a homebrew idea similar to the continuous spectrum, and finally (after 13.67) concludes that they… do not represent physical states of a particle. Is a “non-normalizable state” a quantum state? Or it is a supplementary construction? At last, can anybody say what exactly did L. E. Ballentine write? Incnis Mrsi (talk) 22:11, 9 January 2014 (UTC)

Statistical vs. mixed

The discussion in sec. 2.7 presenting "statistical" and "mixed" as related concepts appears misleading. "Statistical" relates to ensembles, or at least to a partial knowledge about the details of the state of the system (as in fact noted earlier in sec. 1.1). Non-pure (mixed) state can reflect a fundamental quantum-mechanical uncertainty: the entire system can be KNOWN to be in a particular well-defined pure state, yet its subsystem is in a mixed state. Yes, the same density matrix formalism can be used to describe statistical uncertainty, but this does not mean that the nature of a mixed state must be statistical.