Talk:Ladder operator

2005 bad article

Who wrote this? Not only is the spelling bad, but it's wrong! The ladder operators are the creation and annihilation operators. However, I may be wrong. Will someone who is certain please amend this page, or follow this comment up with why I'm wrong? Many thanks.

The titles of Wikipedia articles are usually supposed to be in the singular, and, sure enough, Ladder operator redirects to Quantum harmonic oscillator, which seems to have a more mature discussion of the topic. I have changed Ladder operators to match. - RedWordSmith 01:20, Mar 14, 2005 (UTC)

Although I've never come across an official definition of ladder operators, I have found it standard to define them by their property of mapping between diferent eigenstates of the Hamiltonian. The definition on this page only applies to the oscillator. This page needs serious attention from someone who actually knows wht they are talking about

Raising/lowering vs. creation/annihilation

I feel that it is worth adding a section to clear up to confusion over raising/lowering vs creation/annihilation operators. It seems to me that whether or not they are the same thing is a matter of perspective. I'd appreciate any comments on the following proposed section as I'm not to familiar with the applications of creation/annihilation operators and it is possible I've missed something.--DJIndica (talk) 13:22, 16 April 2009 (UTC)

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Main article: Creation and annihilation operators

There is some confusion regarding the relationship between the raising and lowering ladder operators and the creation and annihilation operators commonly used in quantum field theory. The creation operator a_i^† increments the number of particles in state i, while the corresponding annihilation operator a_i decrements the number of particles in state i. This clearly satisfies the requirements of the above definition of a ladder operator: the incrementing or decrementing of the eigenvalue of another operator (in this case the particle number operator).

Confusion arises because the term ladder operator is typically used to describe an operator that acts to increment or decrement a quantum number describing the state of a system. To perform the same operation with creation/annihilation operators would require the use of an annihilation operator to remove a particle from the initial state and a creation operator to add a particle to the final state.

question about number operator

I see XN|n> equated to Xn|n>. I need an explanation of the two roles played by "n". 211.28.130.58 (talk) 08:28, 12 December 2012 (UTC)

N is an operator. It's eigenvalues are n. It's eigenstates are |n>. 67.198.37.16 (talk) 01:28, 18 December 2015 (UTC)

Dubious

Someone (in April 2015) tagged the following text as dubious, and they are right: I'm removing the text until it is clarified:

"The restriction on $l$ and $m_{l}$ to integer multiples of ħ was done by "H. E. Rorschach at the 1962 Southwestern Meeting of the American Physical Society." There also may have been resistance to such a split by Merzbacher. The ladder operators have been extended many times, to deal with spin, and to generate l.

At face value, the above reads as pure non-sense of some kind. -- it is well known that angular momentum is given by representations of su(2) and any other claims are gobbldy-gook. On closer reading, well, I suppose that maybe someone in 1962 proved some sort of generalized theorem about some kind of general ladder operators outside of the narrow context of the rotation group. (ladder operators are also used in Lie groups, but there the root system was very very well understood well before 1962). Eugen Merzbacher is a respected authority, but I can't tell what he objected to. Ditto Raab, de Lange. So whatever these sentences are trying to say, its so totally unclear, that it sounds like nonsense. So I removed them.

Given the title of Merzbacher's paper, perhaps he was objecting to the double-covering of O(3) by SU(2) which perhaps was not yet widely known in 1962??? I can only guess.

Looking at the article history, the above is all that remained of some text that ... was almost was coherent, e.g. here: March 2012 version. Unfortunately, it wasn't well written to begin with and so the surrounding text was slowly edited into oblivion. It tried to give some interesting historical flavor, which would be nice to have, but it needs to be written much more clearly. 67.198.37.16 (talk) 02:10, 18 December 2015 (UTC)

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References

Typesetting

The typesetting of math symbols in the text is differs from the equations. — Preceding unsigned comment added by Rappel1 (talk • contribs) 08:33, 3 March 2020 (UTC)