Timeline for Harmonic oscillator with heat bath
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 5, 2016 at 15:18 | vote | accept | Darius | ||
| Jan 5, 2016 at 6:20 | answer | added | march | timeline score: 4 | |
| Jan 5, 2016 at 5:51 | comment | added | march | The units are wrong in your last expression. The way to calculate this is to directly compute the trace in the oscillator eigenbasis. That allows you to get rid of $H$ in favor of $n$'s, and the trace turns into a geometric series and the derivative of a geometric series. | |
| Jan 3, 2016 at 15:45 | comment | added | Darius | Now I see, that they are connected by the derivative and a minus. And I can somehow remember, that taking the derivative by $\beta$ would give the energy of the system :) | |
| Jan 3, 2016 at 15:27 | comment | added | udrv | Ok, so calculating the partition function would indeed require use of creation & annihilation ops. It's not hard to do the trace sum though. Assuming you try this, what happens if you take the derivative on $\beta$ of $Tr\left[e^{-\beta H}\right]$? | |
| Jan 3, 2016 at 15:08 | comment | added | Darius | The partition function is not given in the exercise, but we had that topic in thermodynamics, so I guess I could write it down. But sorry, I'm kind of stuck at that point.. | |
| Jan 3, 2016 at 14:35 | comment | added | udrv | Do you know the partition function before hand? Say you do. If you write $e^{-\frac{H}{k_BT}}$ as $e^{-\beta H}$, what relationship do you see between $Tr\left[e^{-\beta H}\right]$ and $Tr\left[H e^{-\beta H}\right]$? | |
| Jan 3, 2016 at 14:29 | history | edited | DanielSank | CC BY-SA 3.0 |
fix weird math formatting
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| Jan 3, 2016 at 14:02 | history | asked | Darius | CC BY-SA 3.0 |