Timeline for Classical limit of quantum systems
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 18, 2010 at 17:04 | comment | added | Ian Durham | So basically you're asking for inequivalent quantum systems that lead to the same classical system. Is that right? The opposite of what Jose suggested in his answer? | |
| Feb 18, 2010 at 10:31 | comment | added | Anirbit | I am asking if there are non-trivial examples where "different" ways of quantizing end up actually giving completely different energy spectrum or giving quantum systems with different classical limits. Or is there an argument/theorem which states that such a thing is impossible? | |
| Feb 18, 2010 at 10:29 | comment | added | Anirbit | I am probably meaning "quantizing something differently using the same method" . Let us keep to canonical quantization. We know that in the simplest example of an harmonic oscillator if the classical hamiltonian is written as product of two complex conjugate numbers and then quantized then the energy spectrum doesn't have a zero-point energy unlike the usual case. Here the two different ways of quantizing only ended up in giving two spectrums shifted from each other by a constant. But the classical limit did not change. | |
| Feb 17, 2010 at 22:13 | comment | added | Ian Durham | I second Ben's comment regarding quantization. I'm not sure what you mean. For example, are you talking about canonical versus loop versus geometric (etc.) quantization or are you talking about quantizing something differently using the same method (e.g. two canonical systems)? | |
| Feb 17, 2010 at 15:24 | answer | added | José Figueroa-O'Farrill | timeline score: 2 | |
| Feb 17, 2010 at 14:42 | comment | added | Ben Webster♦ | <i>But shouldn't it be possible that having quantized a classical system in two different methods in general it should be possible that their "classical limits" are actually different classical systems?</i>- I'm extremely confused about what this could mean. You seem to be suggesting that you could quantize a classical system and get something else as classical limit, which makes me wonder what your definition of "quantization" is. | |
| Feb 17, 2010 at 14:03 | comment | added | Steve Huntsman | Also classical observables commute, so there should be a unique classical system unless I'm being obtuse (also a possibility). The Poisson brackets don't affect this. | |
| Feb 17, 2010 at 14:00 | comment | added | Steve Huntsman | BTW the standard is usually called Weyl ordering: books.google.com/… | |
| Feb 17, 2010 at 11:23 | history | asked | Anirbit | CC BY-SA 2.5 |