Talk:Old quantum theory
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Merge With Bohr Model
Can someone please explain the following phrase:Thermal fluctuations forbid a transition in the oscillator of even one quantum? Isn't thermal fluctuation supposed to cause the transition? Thanks for your help! Thurth 07:18, 4 March 2009 (UTC)
- What the editor probably wants to say, is that the number of quanta having energy equal to the energy differences of the (discrete) oscillator levels gets smaller as temperature gets lower. So, it is not a matter of forbidding; just the transition probability gets smaller (to become zero at the unattainable limit T = 0). If I can find time I will change the text accordingly.WMdeMuynck (talk) 10:07, 4 March 2009 (UTC)
Thanks for the explanation. I am translating this article into Chinese. This paragraph is probably in the area of statistical physics or low-temperature physics. Now, I think I understand the physical process involved and I can continue translate the rest of this article. Thanks again! Thurth (talk) 05:14, 5 March 2009 (UTC)
- The issue played an important role in explanation of unexpected behaviour of specific heat at very low temperatures found experimentally some 100 years ago. The phenomenon indeed requires statistical techniques, but is above all considered as an early proof of quantisation of energy levels.WMdeMuynck (talk) 13:42, 5 March 2009 (UTC)
What this was saying is better stated now, but it's this: In classical mechanics, you have continuous energy. So at temperature T you have energy equal to T. But in quantum mechanics, the energy is discrete. So when T is much smaller than the quantum Q, instead of having energy T, you now only have probability exp(-Q/T) of having one quantum, most of the time you have exactly zero energy. This means that the average value of the energy at large T is indeed proportional to T, but at small T, it's proportional to exp(-Q/T). The Einstein formulas interpolate between the two regimes, much like the Planck formula interpolates between the long wavelength and short wavelength limits.Likebox (talk) 16:39, 5 March 2009 (UTC)
- In answering User:Thurth I had in mind a full-blown quantum mechanical theory in which both radiation and matter are quantized. I agree with you that for the Old quantum theory page it is preferable to restrict an account of specific heat to the semi-classical approach of that period.WMdeMuynck (talk) 13:05, 6 March 2009 (UTC)
Problem with one dimensional linear potential
Please correct me if I am wrong. Based on following statement, This integral is the area under a (sideways) parabola, which is 4/3 the area of an inscribed triangle of height and base , the area of the triagle should be
which if substituted into the equation, should yield quantization rule
- Thanks for pointing out the errors. I am very interested in the section about the Kramers transition matrix. This is quite new to me. Can you provide some references so that I can read more about it? Thanks! Thurth (talk) 22:50, 22 March 2009 (UTC)
- Unfortunately, I don't know much more than what is written. There is a discussion of Kramers/Heisenberg transition calculations in one of the more detailed technical references on the matrix mechanics page. They are ridiculously hard to follow for the modern reader.Likebox (talk) 00:24, 24 March 2009 (UTC)
Specific Heat Formulas
Thermodynamics has mind-numbingly stupid conventions left over from the 19th century, before it was realized that energy is lower level than entropy. Instead of dealing with entropy-like quantities like S,F/kT, G/kT, which are fundamental, they formulate everything in terms of the energy-like quantities E,F,G which is completely idiotic from a statistical point of view. This means that all the thermodynamic potentials are defined incorrectly, especially the temperature.
Instead of this ridiculous form:
The correct form from statistical mechanics is
It's not equivalent, since, for example, a maxwell relation tells you that
which looks nontrivial when expanded out by product rule and chain rule. In the correct statistical mechanics form, all thermodynamic relations are trivial.
This means that physicists just ignore thermodynamic tradition nowadays, and often use their own conventions for the quantities. Beta is 1/T, mu is mu/T etc. Most of the difficulty in learning thermodynamics is learning that the second derivative with respect to beta is not the same as the second derivative with respect to T.
Since the whole language of thermodynamics is fundamentally broken, disguising its essential triviality behind a ridiculous set of bad changes of variables, I think that most physicists would prefer if it were never mentioned at all. This is why I erased the formula for Cv.Likebox (talk) 14:49, 26 June 2009 (UTC)