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Electron in B Field  Quantum 
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#1
Nov2110, 11:24 AM

P: 281

1. The problem statement, all variables and given/known data
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. 3. 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 zdirection we could write B as a scalar and we'd just find the eigenvalues of the third pauli matrix. 


#2
Nov2110, 12:35 PM

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P: 11,670

It's all three components
[tex]\hat{S} = \hat{i}S_x + \hat{j}S_y + \hat{k}S_z[/tex] Take the dot product as usual and then you can express the Hamiltonian as a linear combination of the Pauli matrices. 


#3
Nov2110, 06:24 PM

P: 281

cheers for that, cleared it up.



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