Timeline for Confusion in Quantum Harmonic Oscillator
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 18, 2021 at 7:05 | answer | added | Ricky Pang | timeline score: 0 | |
| Jul 15, 2021 at 15:35 | comment | added | Ricky Pang | Thanks @KP99. I have the same point of view after reading M. Schwartz QFT. The number of particle in field theory sense means the total number of excitation modes. If we treat the excitation modes as the particle number, then $n$ really means the number operator which governs the particle number of the system, which is different from the classical sense. | |
| Jul 15, 2021 at 15:30 | comment | added | KP99 | In the comment after eqn (2.44), he mentions that ket $|p\rangle$ refers to eigenstate of single particle. He then carries over the same notations in multi-particle states and defines the number operator N which measures sum of excitation states for each particle for a given multi-particle state. Actually here N refers to the number of "virtual particles" and not the real particles. | |
| Jul 15, 2021 at 15:01 | history | edited | Vincent Thacker | CC BY-SA 4.0 |
deleted 45 characters in body; edited tags
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| Jul 15, 2021 at 14:58 | comment | added | Ricky Pang | Hi, @KP99, thanks for your comment. Yes, in the sense of simple quantum harmonic oscillator, I agree that the number operators counts for the excitation states. However, in QFT[Prof. D. Tong Notes (p.31) ](damtp.cam.ac.uk/user/tong/qft/qft.pdf), the number operator commutes with the Hamiltonian ensuring that particle number is conserved. That's why I am confused with the meaning of particle number in that simple model. | |
| Jul 15, 2021 at 14:52 | answer | added | Physiker | timeline score: 1 | |
| Jul 15, 2021 at 14:40 | comment | added | KP99 | Eigen values of the number operator denotes the excitation states, not the particle number | |
| Jul 15, 2021 at 14:39 | comment | added | Ricky Pang | Yes, it is one-body Hamiltonian. But I am confused with that if the eigenvalues of number operator $\hat{n}$ is $0,1,2,\ldots,N$, why the Hamiltonian is called one particle Hamiltonian. I am new to condensed matter physics and I always got confused with the definition of many body Hamiltonian or single-particel Hamiltonian. | |
| Jul 15, 2021 at 14:33 | history | asked | Ricky Pang | CC BY-SA 4.0 |