Recent content by pogs

Ok thanks.

Ok, but you're not really answering my question. What about the eigenspinors of ##S_x## then? Under what conditions would I be expected to use them?

The first part of the question only asks whether we have an eigenstate and what the eigenvalue is aka. If its not an eigenstate THEN you calculate the expectation value. I'm asking when I apply the operator to the wavefunction how am I supposed to know which spinor I use.

I understand what the convention is, I'm trying to get clarity on when one is supposed to use the S_x eigenspinors. What you seem to be saying is the fact that I'm measuring ##S_x## has no bearing on the spinors I use. So when would you be expected to use the ##S_x## eigenspinors? Is it only...

Thanks both. Hutch, in regards to your point I'm actually asked to assess $$S_x \psi_{c} = S_x (\frac{1}{\sqrt3}\psi_{321\downarrow} + \sqrt{\frac{2}{3}}\psi_{321\uparrow})$$ So to me its really not clear which spinor I should be using and why.

Thanks again Kuruman Maybe you can help me interpret the question then. How am I supposed to define spin down here? As far as I can tell there are two different possible ways. Part two. Whilst I'm grateful for your help, please don't tell me its not hard to understand, its an unnecessary...

Thanks again Kuruman In general, when we are asked to find the effect of the ##S_x## operator on some wave function am I to assume we use the eigenspinors for ##S_x## applied to the wave function spin state? and if so why exactly? Why not, use the Pauli matrix applied to the spin down vector...

Ah yes, thanks for the help, its a typo but also a wrong calculation. Also the second part has a missing vector. It should be $$S_x = \frac{\hbar}{2} \begin{bmatrix} 0 & 1\\ 1 & 0 \end{bmatrix} \psi_{321\downarrow} = \frac{\hbar}{2} \begin{bmatrix} 0 & 1\\ 1 & 0 \end{bmatrix} \frac{1}{\sqrt2}...

Brilliant thanks Doc. So to continue the question for ##J_z + L_z + S_z## If I try to make it more general I think I get the following, is it correct? Do we just use additivity? $$J_z f^l_m = (L_z + S_z) f^l_m \implies J_z f^l_m = (\hbar m + \hbar m) f^l_m$$ Then for ##\psi_a## and...

great thanks Oroduin, can you comment on the last part of the question too please?

OK, that makes sense, thanks very much, and yes it was the addition of angular momenta for a two particle system, my mistake. For the third state ##\psi_c = \sqrt{\frac{1}{3}}\psi_{211\downarrow} + \sqrt{\frac{2}{3}}\psi_{210\uparrow}## ##m_1 \neq m_2 ## so I would guess its not an eigenstate...

But looking at Griffiths book on Quantum mechanics edition 3 p.176 eq.4.174 $$m = m_1 + m_2$$ So ##m_1 = m_2 = 1## ##\implies m =2## no? I guess you're suggesting I leave the m's for each state as they are like so. $$L_z \frac{1}{\sqrt2}(\psi_{321\downarrow}+ \psi_{321\uparrow}) =...

Thanks Dr Claude. I tried editing my question in the homework statement but I hope you can see the LaTex still isn't displaying, but it works elsewhere... So if I apply Lz to the state I should get back the state times ##\hbar m## correct? $$L_z \psi_{nmls} = \hbar m \psi_{nmls}$$ In this...

I'm really not sure what the question expects me to do here but here is what I do know. If the state is an eigenstate it should satisfy the eigenvalue equation for example; $$\hat{H} f_m^l = \lambda f_m^l$$ but is the question asking me to use each operator on each state? How do I know if...

Attempt at solution: I wanted to try and solve this with dimensional analysis. I reasoned that I would chose the following dependent variables: - [V] : Volume ( of the block) - [Q] : Heat ( the radioactive decay would cause some heating of the water) - [R]: Radiation - [Cv]: Heat capacity...