1. A Mass eigenstates

Does saying "states of definite mass" is the same as saying "mass eigenstates"?

Hey everyone, I've been doing some quantum mechanics but I think I have yet to fully grasp the meaning of eigenstate. What I mean is, I understand that an eigenstate ##x## is such that, if we have an operator ##\hat{A}##, it satisfies ##\hat{A} x=\lambda x## and so ##\hat{A}## represents a...
3. Commuting Operators

Homework Statement It is known that ##M_1,M_2, M_3## commute with each other but I don't see how the second line is achieved even though it says that it's using that ##M_1## and ##M_2## commute?
4. A Eigenstates of "summed" matrix

Hi to all. Say that you have an eigenvalue problem of a Hermitian matrix ##A## and want (for many reasons) to calculate the eigenvalues and eigenstates for many cases where only the diagonal elements are changed in each case. Say the common eigenvalue problem is ##Ax=λx##. The ##A## matrix is...
5. 'Symmetry argument' for eigenstate superposition

Homework Statement For an infinite potential well of length [0 ; L], I am asked to write the following function ##\Psi## (at t=0) as a superposition of eigenstates (##\psi_n##): $$\Psi (x, t=0)=Ax(L-x)$$ for ## 0<x<L##, and ##0## everywhere else. The attempt at a solution I have first...
6. Instantaneous eigenstates in the Heisenberg picture

I'm a bit confused as to what is meant by instantaneous eigenstates in the Heisenberg picture. Does it simply mean that if vectors in the corresponding Hilbert space are eigenstates of some operator, then they won't necessarily be so for all times ##t##, the eigenstates of the operator will...
7. Eigenstates of 3 spin 1/2 particles

Hi, I have learned about how to find the 4 spin states of 2 spin 1/2 particles, and how to find them by using the lowering operator twice on |1/2, 1/2> to find the triplet, then simply finding the orthogonal singlet state, |0, 0>. I started to attempt finding the states of 3 spin 1/2...
8. Electron Clebsch-Gordon coefficients

Homework Statement The state of an electron is, |Psi> =a|l =2, m=0> ⊗ |up> + Psi =a|l =2, m=1> ⊗ |down>, a and b are constants with |a|2 + |b|2 = 1 choose a and b such that |Psi> is an eigenstate of the following operators: L2, S2, J2 and Jz. The attempt at a solution I am really not...