Timeline for Schrödinger equation for a harmonic oscillator
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 30, 2013 at 12:04 | comment | added | Eugene B | My favourite is Nouredine Zettili, but you can find it in any good QM book. | |
| Apr 30, 2013 at 11:24 | vote | accept | 71GA | ||
| Apr 30, 2013 at 11:21 | comment | added | 71GA | Thank you. Where can i read more about Bra-Ket notation you used in the added derivation? I don't know how i can interpret this $ \hat{a}^\dagger \left| n \right\rangle = \sqrt{n + 1} \left| n + 1 \right\rangle$ | |
| Apr 30, 2013 at 10:06 | comment | added | Eugene B | The answer on your first question is simple and is already in your question: because it's constant! your commutator is nothing but $ab - ba$, but if there is some constant factor $c$, you can easily write $cab - bca = cab - cba = c (ab - ba)$. I have also edited the main answer and added the derivation you've requested there. | |
| Apr 30, 2013 at 10:03 | history | edited | Eugene B | CC BY-SA 3.0 |
Added derivation of eigenvalue of the number operator.
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| Apr 29, 2013 at 20:08 | comment | added | 71GA | Ok so i have come to the end of your derivation and all i need to know is two things. 1st: Why can we factor out constant $1/(x_0 y_0)$ when calculating a commutator $\left[\hat{X},\hat{P}\right]$ and 2nd: I need some sort of a proof that $\hat{N} = \hat{a}\,\hat{a}^\dagger$. | |
| Apr 29, 2013 at 19:15 | comment | added | Eugene B | How could I have forgot about my favourite book! In quantum mechanics Nouredine Zettili is the best of I ever tried. | |
| Apr 29, 2013 at 18:25 | comment | added | Eugene B | It comes from the commutation relation between position and momentum operators. It is easy to derive and shall be your homework :-) | |
| Apr 29, 2013 at 18:22 | comment | added | 71GA | Can i ask where did you use the commutator relation between $\hat{X}$ and $\hat{P}$? Does an $i$ means their order i need to multiply that by an $i$? | |
| Apr 29, 2013 at 17:57 | comment | added | Eugene B | Also, you can spend some time googling for lecture notes (there are plenty of them as well as of examples) and select those you prefer. To be honest, I have never had difficulties at this point, therefore haven't mined literature, just solved problems from Schaum's. Really, it all depends on your learning style and on amount of spare time you have. | |
| Apr 29, 2013 at 17:54 | comment | added | Eugene B | It depends on your situation: if you are high school guy learning quantum mechanics for fun, then you will be fine :-) if you are second year undergrad having exams this week, then you definitely stuck. It is impossible to learn further quantum mechanics without these concepts. Depending you your learning style, I might recommend Schaum's Outlines series -- if you like learning stuff by solving on your own; Arfken of Riley -- if you prefer dense explanation with derivations. Actually, these are not mutually exclusive, so you can make use of both (three, actually). | |
| Apr 29, 2013 at 17:39 | comment | added | 71GA | Thank you very much for all your effort! I will need some time to digest this as it is a big leap for me. I have been avoiding eigenvectors and eigenvalues untill now, but suprisingly i managed to understand every single thing until this one. Could you point me to any good video/book explaining eigenvalues or eigenvectors? I am allso unfamiliar with commutators... Am i in a big trouble? | |
| Apr 29, 2013 at 16:16 | history | answered | Eugene B | CC BY-SA 3.0 |