Timeline for When is the vibration energy quantized?
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11 events
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| Jul 19, 2020 at 9:54 | comment | added | hbadger19042 | Thanks for the links, anna. I would study more seriously. I hoped I could find more fundamental answers than the philosophy of 'it works'. I thought all the quantization would be connected somehow. maybe something like Noether's theorem for symmetry. | |
| Jul 18, 2020 at 12:57 | comment | added | anna v | The wuantized energy levels in solving for molecules with the harmonic potential assumption have nothing to do with field theory. It is a successful computational way for energy levels. Note that all symmetric potentials if expanded have a $x^2$ as the first temr, i.e. a harmonic oscilator first term, that is the usefulness when solving equations with a potential. For QFTs there are no potentials (except the example of the harmonic in order to understand creation and annihilation) | |
| Jul 18, 2020 at 12:53 | comment | added | anna v | If you are serious in studying physics you could try the MIT open courses ocw.mit.edu/courses/physics . Quantum field theory is a quantum mechanical tool that has many appications, from condensed matter to nuclear physics and ofcourse to particle physics. please see this answer of mine physics.stackexchange.com/questions/565868/… and this physics.stackexchange.com/questions/563106/… | |
| Jul 18, 2020 at 12:26 | comment | added | hbadger19042 | I feel a huge gap between the quantization of harmonic oscillator and field quantization in QFT. QFT is to quantize the field of fundamental particles but the harmonic oscillator is to quantize complicated molecules. I don't know how the quantization can work for both cases. I felt that the quantization was not the property of constituent of the system. But the vibration energy is quantized somehow. They even talk about the quantization of the vibration energy of the vacuum. (Though I don't know what they are talking of with the vacuum.) | |
| Jul 18, 2020 at 11:51 | comment | added | anna v | generally classical equations' and quantum mechanical equations' are a different story. | |
| Jul 18, 2020 at 11:05 | comment | added | hbadger19042 | I think the violin string example is a bit different story. The frequency is quantized, but the amplitude is not and so not the energy either while the harmonic oscillator's energy is quantized with its fixed resonance frequency. | |
| Jul 18, 2020 at 10:22 | comment | added | anna v | In order to have a macroscopic quantum effect all the zillions of wavefunctions should be coherent, at least in some projection, The vibrations of the classical oscillator have nothing to do with the case.. Take a violin string, you could call the main and harmonics "quantum", because they come in steps, but it has nothing to do with the quantum state of the individual molecules vibrating altogether . | |
| Jul 18, 2020 at 10:16 | comment | added | hbadger19042 | With the superfluidity and superconductivity, the molecules attending the phenomenon are quantized. I think it would be more related to the condition if the molecules show the permutation symmetry for the spin-statistics theorem. But with the quantization of harmonic oscillator, it seems the molecules attending to the phenomenon doesn't matter. The quantization of the harmonic oscillator seems more concerned with the vibrational energy of the system as a whole. Am I understanding in the wrong way? | |
| Jul 18, 2020 at 10:15 | history | edited | anna v | CC BY-SA 4.0 |
clarification
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| Jul 18, 2020 at 8:50 | history | edited | anna v | CC BY-SA 4.0 |
added 44 characters in body
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| Jul 18, 2020 at 8:43 | history | answered | anna v | CC BY-SA 4.0 |