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1. I Total angular momentum for antiparallel electrons

Oh, Yes. You're absolutely right. I was confused. Yes, for two electrons in a partially filled subshell or different subshells or even free states, we really don't know a definite value of total spin projection quantum number ms for these electrons before its measurement, unlikely to CS (Closed...
2. I Common eigenfuctions for degeneracy

Hello. I found and studied a simpler proof of existence (always exist) of a set of common eigenfunctions for commuting operators in degeneracy. I uploaded this so other people who have a similar question can refer.
3. I Common eigenfuctions for degeneracy

Am...I'm afraid that my statement gives a possibility of wrong interpretation. In my statement of "for compatible (commuting) operators {A, B}, we can always find a set of common eigenfunctions of all eigenvalues of both operators", "eigenfunction of all eigenvalues of both operator" does not...
4. I Common eigenfuctions for degeneracy

Hello. Your answer is far more complicated than I expected. It was a long time ago that I studied matrix representation of operators. But of course, I'll re-study this for reminding to understand your comments. Before doing that, I just want to gett an answer of one question: is statement of...
5. I Common eigenfuctions for degeneracy

Hello. I read the textbook and found that common eigenfunctions are even possible for degenerate eigenvalues. Let's say operators A and B commutes and eigenvalue a of operator A is N-fold degenerate, means that there are N linearly independent eigenfunctions having same eigenvalue a. These...
6. I Total angular momentum for antiparallel electrons

Hello. I appreciate your effort to follow all kinds of questions that I have posted. Thank you. Right now, I'm thinking that the question about "pairing electrons in a PS (Partially filled Subshell)" doesn't make sense at all. We're talking about angular momentum (and spin)-related total...
7. I Total angular momentum for antiparallel electrons

Thanks for giving me some answer. Let me summarize your comment. So, the fact that the total orbital QN (Quantum Number) l for CS (Closed Subshell) is always zero stems from a requirement that total magnetic QN m is zero for CS; no other value than 0 is allowed for m (a sum of individual...
8. I Total angular momentum for antiparallel electrons

PeterDonis indicates same things as you mentioned. I would be happy if you follow his last post and my last reply to him and give me some comments:)
9. I Total angular momentum for antiparallel electrons

Oh Yes!! You're touching the heart of my confusion! I thought that CS (Closed Subshell) and the situation that all electrons are paired are equivalent. "electrons are paired" here means that if there is an electron with an individual magnetic QN (Quantum Number) mli = a and individual spin...
10. I Total angular momentum for antiparallel electrons

Hello. These are a reference I can give you. 1. http://quantummechanics.ucsd.edu/ph130a/130_notes/node36.html 2. https://www.researchgate.net/post/Why_are_total_orbital_quantum_number_l_and_total_magnetic_quantum_number_m_zero_for_closed_subshell [Broken] It looks that you think total...
11. I Total angular momentum for antiparallel electrons

Hello. I'm sorry why you said m = 0 must be "possible" for CS. I think the fact is that m = 0 is only one possible case for CS.
12. I Total angular momentum for antiparallel electrons

What...? Reference? I've seen that L = S = 0 for CS (Closed Subshell) many times in various sources. I think it is commonly said, although I'm not fully understanding the exact reason of this. You can easily find this fact by googling.
13. I Total angular momentum for antiparallel electrons

Hello. Thanks for replying my question. I know that magnetic quantum number m can be zero for other orbital quantum number l. In my question, I meant that l = 0 is the only case which allows "only" m = 0. I had been confused why total orbital quantum number l for a CS (Closed Subshell) is...
14. I Total angular momentum for antiparallel electrons

Hello. Let's have two electrons with same orbital quantum number li and these electrons are in antiparallel; one electron has magnetic quantum number mi = a and and other electron has mi = -a (but we don't know which one has ml = a as we're in coupled representation to talk about total angular...
15. A Wave of an outgoing anti-particle in quantum field theory?

Hello. I'm studying a course of the Quantum Field Theory and I got a question in a canonical quantization of a scalar field. I don't write a full expression of the field quantization here but the textbook said terms with ei(p⋅x - Ept) are associated with an incoming particle and terms with...
16. I Why is association rule in angular momentum sum not valid?

This is actually Korea book so you may not know this. Not famous book but it shows this relation with some proof which is...difficult for me to understand. Have you ever seen this relation? I think essence is this; total angular momentum quantum number J resulted from LS coupling is different to...
17. I Why is association rule in angular momentum sum not valid?

Hello. The quantum mechanics textbook shows the relation of J1 + J2 + J3 ≠ J1 + (J2 + J3). I believe Ji is total angular momentum operator for ith group of electrons (but actually I have not seen J1 operator while I have seen J12 operator so far). I don't know how to prove J1 + J2 + J3 ≠ J1 +...
18. I Why are total orbital QN l,m zero for closed subshell?

I see. I was actually trying to get total orbital number l in uncoupled representation while l can be specified only in coupled representation. I did action of contradiction. Thanks to correct my mind! I appreciate it!
19. I Why are total orbital QN l,m zero for closed subshell?

Hi. I think your argument is weak to explain total orbital quantum number l = 0 for closed shell. The essence of your argument is that total magnetic quantum number m has only one value for given states of individual electrons. Let's get the case that there are two electrons, (l1 = 1, m1 = -1)...
20. I Why are total orbital QN l,m zero for closed subshell?

Am...I thought closed subshell is common word in quantum mechanics. It is completely filled subshell specified by n and l. For a given closed subshell nl, all states specified with m and ms under nl are completely filled. SO could you please simplify your comments for this case?
21. I Why are total orbital QN l,m zero for closed subshell?

Hello and thank you to reply this question. So...there is no mathematical proof that total orbital quanum number l is zero for closed subshell in atom but it is from physical thinking?
22. I Could you provide me a selection rule?

Hello. Thanks to give me comment. Is L and S are total orbital quantum number (azimuthal quantum number) and total magnetic quantum number respectively while l is orbital quantum number for each electron state? And can you tell me what literature or article is used for suggesting these rules? I...
23. I Spontaneous Absorption

I'm not expert at all about Quantum Mechanics but I have to ask what spontaneous absorption means? The term "spontaneous" is used typically to indicate some event which occurs without external induction. I also heard that the spontanoue emission is yes, induced by vacuum field fluctuation...
24. I Why are total orbital QN l,m zero for closed subshell?

Hello. Here, I'm asking why total orbital quantum number l and total magnetic quantum number m are zero for closed subshell in atom. Let me review the addition of angular momentum first: Each electron has its own orbital quantum number li and magnetic quantum number mi. Then for two electrons...
25. I Could you provide me a selection rule?

Hello. When I accessed to selection rule page in Wikipedia, I have a difficulty of how to use rules listed there. I'm now only concering electric dipole transition so column (E1) in the table there will be my only interests. Since I need to know whether transition is possible or not between...
26. How Fourier components of vector potential becomes operators

Hello. I'm studying quantization of electromagnetic field (to see photon!) and on the way to reach harmonic oscillator Hamiltonian as a final stage, sudden transition that the Fourier components of vector potential A become quantum operators is observed. (See...
27. What happens on un-ionized electrons after ionization?

Okay. It looks definitely true that the remaining electrons should go to occupy new bound states according to new Hamiltonian after ionization but..to occupy new states which enery level is higher than old? It is possible? It looks the violation of the energy! How it is possible?
28. What happens on un-ionized electrons after ionization?

Answer looks complocated to understand. Thus..the states of the N-1 bound electrons are different from N electron case right?
29. What happens on un-ionized electrons after ionization?

Hello. I'm now working in the spectroscopy and I'm wondering in one instantaneous moment of ionization. Let's have an atom with multiple bound electrons. The external energy (like in form of photon) is introduced on the atom such that outer bound electron is ionized and the question...
30. What is wavefunction in the time-dependent schrodinger equation?

Thus are you saying that the time-dependent Schroedinger equation has solution which is eigen function of the Hamiltonian and angular momentum eigenfunction is also possible solution for this equation since the angular momentum operator is commuted with Hamiltonian?