Timeline for Modified quantum harmonic oscillator: hamiltonians unitarily equivalent and energy spectrum
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15 events
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| Dec 18, 2022 at 23:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 20, 2022 at 6:03 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 18, 2022 at 5:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 17, 2021 at 20:04 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Aug 19, 2021 at 4:07 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Apr 29, 2020 at 12:46 | answer | added | PPIP | timeline score: 1 | |
| Jan 16, 2020 at 20:03 | comment | added | Artem Alexandrov | I am not sure, I just suggest | |
| Jan 16, 2020 at 19:58 | comment | added | dfgoe55 | Why you said that in term of creation-annihilation operators the equivalence is obvious? How can I prove that? | |
| Jan 16, 2020 at 17:17 | comment | added | dfgoe55 | I have used the canonical commutation relations between $q$ and $p$ to rewrite the term $(pq^2 + q^2p)$ but the problem is that the constant I have written is a complex number and therefore the energy of the system is shifted by a complex quantity, that is obviously wrong. | |
| Jan 16, 2020 at 17:04 | comment | added | Artem Alexandrov | What is $\hbar$? How does it appear? | |
| Jan 16, 2020 at 16:31 | comment | added | dfgoe55 | I put the Hamiltonian in this form $H = (\frac{p}{\sqrt{2m}} + \sqrt{\frac{m}{2}} q^2)^2 + (\frac{m}{2} \omega q + \frac{\alpha + i \hbar \beta}{\omega \sqrt{2m}})^2 - constant^2$. Under an proper change of variables It seems that is the Hamiltonian of a quantum harmonic oscillator without any strange term. | |
| Jan 15, 2020 at 17:32 | comment | added | Artem Alexandrov | It is useful to start from the rewriting hamiltonian in terms of creation-annihilation operators. This makes Hamiltonian more clear but consumes lot of time. It seems that you should use perturbation theory but if you provide the text of the problem may be it ll be useful. Also, if you rewrite Hamiltonian in terms of creation-annihilation operators, it seems that equivalence is obvious | |
| Jan 15, 2020 at 17:26 | history | edited | lurscher |
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| Jan 15, 2020 at 17:20 | review | First posts | |||
| Jan 15, 2020 at 20:34 | |||||
| Jan 15, 2020 at 17:16 | history | asked | dfgoe55 | CC BY-SA 4.0 |