- #1
JesseC
- 251
- 2
Homework Statement
Magnetic field in xz plane.
[tex] \vec{B}=\hat{i}B_x+\hat{k}B_z [/tex]
Write down the hamiltonian operator for the interaction of the electron's intrinsic magnetic moment with this field and express it in matrix form. Find its eigenvalues and sketch these as a function of Bz, for fixed, nonzero Bx. How would the picture differ if Bx were zero.
The Attempt at a Solution
So I got the hamiltonian looking like this:
[tex] \hat{H}= \frac{e g_s}{2m_e} \hat{S} \cdot \vec{B} [/tex]
I'm not sure about the form of [tex]\hat{S}[/tex] in this case? Is it a combination of z and x components?
Normally if the field is just constant in the z-direction we could write B as a scalar and we'd just find the eigenvalues of the third pauli matrix.