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1. ### Spin-Orbit Coupling

Sorry, the electron's orbital momentum points in the same direction of the magnetic field. Thanks!
2. ### Spin-Orbit Coupling

Yes the period the same. But The direction of the angular momentum is parallel to the direction of the magnetic field, then the electron orbital momentum vector should point to the opposite direction?
3. ### Spin-Orbit Coupling

I though the periodic time and the radius of the rotation are affected by the relativistic motion, so the periodic time from the point view of the electron will be different from the point view of the proton.
4. ### Time-dependent Perturbation Theory

He said he is going to use a process of successive approximations, I am not familiar with the "asymptotic expansion" so I can not tell if this what he did
5. ### Time-dependent Perturbation Theory

In equation [9.15] ##c_a(0) = 1## this is before the perturbation (at time ##t= 0##) no transition happened yet and the particle still in the upper state ##a##. But equation [9.17] after perturbation at time t and ca(1)(t) = 1 is the first-order correction. I understand that the zeroth-order...
6. ### Time-dependent Perturbation Theory

He used a process of successive approximations, so for this two particle system the particle starts at state ##a##, then at time t=0: ca(0)=1 and cb(0)=0. If there were no perturbation the system will stay there forever, so we can say the zeroth- order terms are: ca(t)=1 and cb(t)=0. To...
7. ### Time-dependent Perturbation Theory

I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-Dependent Perturbation Theory, Section 9.12. I could not understand that why he put the first order correction ca(1)(t)=1 while it equals a constant.
8. ### Two spin half particles

I only studied two spin half particles from the book Introduction to Quantum Mechanics by David J. Griffiths. I do not know if this enough For example see the attached picture.
9. ### Two spin half particles

for S^2 I will say: S^2=(S1+S2)^2= (S1)^2 + (S2)^2 +2S1.S2 where S1.S2=Sx1Sx2+Sy1Sy2+Sz1Sz2 and add all these 4x4 matrices together to find S^2
10. ### Two spin half particles

For Sz: I added the two 4x4 matrices together: Sz1 + Sz2 and I got 4x4 diagonal matrix with diagonal elements: hbar, 0, 0, hbar.
11. ### Two spin half particles

The problem is I am not familiar with this type of product using this symbol: \otimes ! So will it be wrong if I used the way I described above a got the correct matrices?
12. ### Two spin half particles

Yes this what i mean.
13. ### Two spin half particles

I am looking for 4x4 matrices.
14. ### Two spin half particles

I have this homework: consider the case of two spin half particles. Use the basis: |++>, |+->, |-+>, |--> to find the matrices representing the operators S^2 and S_z. My idea for the solution for S_z is: S_z=S_z(1)+S_z(2) where S_z(1) is the operator for the first particle ... etc So I...
15. ### A Process of Successive Approximations

It worked now, but I equated the the first order of ##\epsilon## (in the left side) with the zeroth order of ##\epsilon ## (in the right side) because the right side is multiplied by ##H^{'}## which is small (of the same order of ##\epsilon##). For example for the first order of ## \epsilon## i...
16. ### A Process of Successive Approximations

I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-Dependent Perturbation Theory, Section: Two-level system. Every thing was fine till He said He will solve this equation: by a process of successive approximations. I have no idea what this...
17. ### Spin-Orbit Coupling

I was reading in the Book: Introduction to Quantum Mechanics by David J. Griffiths. In chapter Time-independent Perturbation Theory, Section: Spin -Orbit Coupling. I understood that the spin–orbit coupling in Hydrogen atom arises from the interaction between the electron’s spin magnetic moment...
18. ### Operator acts on a ket and a bra using Dirac Notation

It is clear now. It seems to me that I need to educate myself and study more in linear algebra. Thank you for your help!
19. ### Operator acts on a ket and a bra using Dirac Notation

Can we say that if the operator is Hermitian then: <ψ| A |Φ> =<Φ| A |ψ>*= a <Φ | ψ>* = a <ψ | Φ> ?
20. ### Operator acts on a ket and a bra using Dirac Notation

I am not sure if this is true or not.
21. ### Operator acts on a ket and a bra using Dirac Notation

If A is Hermitian then the eigenvalue (a) is a real number.

24. ### Operator acts on a ket and a bra using Dirac Notation

Summary:: Operator acts on a ket and a bra using Dirac Notation Please see the attached equations and help, I Think I am confused about this