Timeline for Do the number operator and general Hamiltonians commute?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20, 2023 at 16:18 | comment | added | Tobias Fünke | I guess there are some experts here which can elaborate much more and better than me. | |
| Apr 20, 2023 at 16:18 | comment | added | EE18 | @TobiasFünke Yes, I believe so, thank you! | |
| Apr 20, 2023 at 16:12 | comment | added | Tobias Fünke | I've edited my previous comment. What is important to note that $H$ here refers to the Hamiltonian of the system (as also the answer of the user ReasonMeThis states in the first link). So you are right that depending on the physical situation at hand, it might not be true that the Hamiltonian conserves the particle number, which @Roger Vadim in the same post also points out. Does that clarify some things? | |
| Apr 20, 2023 at 16:06 | comment | added | EE18 | @TobiasFünke Sorry, are you referring to the answer by Roger Vadim or ReasonMeThis? | |
| Apr 20, 2023 at 16:03 | comment | added | Tobias Fünke | ...as the most upvoted answer in the second link states: If you want to describe equilibrium conditions, such that the density operator is constant in time, you are forced to conclude that $H$ preserves the particle number (in the context of the grand canonical ensemble) as long as $\mu \neq 0$. | |
| Apr 20, 2023 at 16:02 | comment | added | Tobias Fünke | I really like the operational approach of the author, also in the context of QM. But IMHO it is, for a physicist at least, supplementary, because he does not discuss many things usual QM (intro) courses discuss (but instead discusses many things not found in "standard" books). Anyway: Yes, I mean if you have a system where the Hamiltonian does not conserve the particle number (say through creation or annihilation of particles), then its does not commute with the respective number operator. So yes, you basically have to assume this... | |
| Apr 20, 2023 at 15:56 | comment | added | EE18 | It is superb, thank you again for the suggestion! Is his QM book worthwhile/at the level of Ballentine too? Also, I'm not sure I completely follow the answers in your links (none were accepted by their respective OPs); is the conclusion I am to derive that Rau is simply assuming a system for which $[\hat{H},\hat{N}] = \hat{0}$ is true? @TobiasFünke | |
| Apr 20, 2023 at 15:16 | comment | added | Tobias Fünke | See e.g. this and this. | |
| Apr 20, 2023 at 15:15 | comment | added | Tobias Fünke | Glad you like the book ;) You can also try out his QM book... Anyway, this was asked before, let me search the relevant PSE posts. But what kind of restrictions do you mean? The only answer I can imagine is: The Hamiltonian must preserve the particle number (and thus commute with the number operator). | |
| Apr 20, 2023 at 15:08 | history | asked | EE18 | CC BY-SA 4.0 |