Timeline for Relativistic generalization of Quantum Harmonic Oscillator
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Jan 13, 2023 at 10:25 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Jan 13, 2023 at 10:15 | answer | added | Roger V. | timeline score: 1 | |
| Jan 13, 2023 at 9:40 | history | edited | Qmechanic♦ | CC BY-SA 4.0 |
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| Jan 13, 2023 at 9:29 | answer | added | Evgeniy | timeline score: 0 | |
| Jul 15, 2013 at 11:10 | history | tweeted | twitter.com/#!/StackPhysics/status/356732560224698368 | ||
| Apr 23, 2013 at 6:57 | history | edited | WInterfell | CC BY-SA 3.0 |
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| Apr 22, 2013 at 19:42 | comment | added | Peter Kravchuk | Moreover, I think that your hamiltonian in $\alpha$ and $\beta$ matrices is not obviously the correct square root -- $m$ and $p$ do not commute. Finally, these matrices are some non-commuting operators, not initially present in the theory -- you are introducing new degrees of freedom, specifically spin. Just thought that it can be not exactly what you want. | |
| Apr 22, 2013 at 19:33 | comment | added | Peter Kravchuk | Your hamiltonian should have $m^2 c^4$. Also I would suggest that you can try to find (and I believe you will succeed) the eigenvalues and eigenstates of the operator under the square root. On the first thought, $H=\sqrt{Q}$ and $Q$ should have the same eigenvectors and correspondingly related eigenvalues. Note the reasoning behind the Klein-Gordon equation. You should also keep in mind that you should be carefull with physical interpretation of your results -- relativistic QM is not totally physically consitent and should be replaced with QFT. | |
| Apr 22, 2013 at 17:56 | history | edited | WInterfell | CC BY-SA 3.0 |
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| Apr 22, 2013 at 16:57 | comment | added | WInterfell | You are right.Changed it. | |
| Apr 22, 2013 at 16:56 | history | edited | WInterfell | CC BY-SA 3.0 |
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| Apr 22, 2013 at 16:53 | comment | added | Luboš Motl | Just a terminological comment, not just questioning your wording but the wording in the aforementioned paper as well. "Harmonic" is something that is composed of sines and cosines (the solutions to the motion of the oscillator in this case). If the solutions aren't sines and cosines, e.g. because the energy isn't simply quadratic, one shouldn't call it "harmonic" oscillator. It's a relativistic generalization of the harmonic oscillator. | |
| Apr 22, 2013 at 16:46 | history | asked | WInterfell | CC BY-SA 3.0 |