Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

I am trying to find the time dependent expectation value for J ($\langle J(t) \rangle$) for a spin 3/2 particle in a uniform magnetic field (in the z direction). My method is as follows: $$H=-\frac{\mu B}{\hbar}J_z$$ Then to find the equaions of motion for $J_i$: $$i\hbar \dot J_i=[J_i,H]$$ $$\dot J_x=\mu B/\hbar \space \space J_y$$ $$\dot J_y=-\mu B/\hbar \space \space J_x$$ $$\dot J_z=0$$ Now I am given tha t the particle is initially in an eigenstate of $J_x$, with eigenvalue +3/2$\hbar$. So I know that: $$J^2|j,m\rangle=\frac{15\hbar^2}{4}|j,m\rangle$$ $$J_x|j,m\rangle=3/2 \hbar|j,m\rangle$$ So to calculate $\langle J(t) \rangle$, I need to know the equations, which I have solved. But then I need to know what $J_y,J_z$ acting on $|j,m\rangle$ is. For the z component of J. $$\langle J_z(t)\rangle=\langle j,m|J_z(0)|j,m\rangle$$ In order to find what $J_z(0)$ is, do I have to create a new raising operator, which would be $Jy\pm iJ_z$ and then find what I initially have in terms of J squared and the x component?

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.