Berry phase of 1/2 spin in slowly rotating magnetic field

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Homework Statement


upload_2017-9-28_14-59-23.png


Homework Equations


upload_2017-9-28_15-4-20.png


This is the way to solve when magnetic field B is arbitrary direction one.

The Attempt at a Solution


upload_2017-9-28_15-0-2.png


I got a eigenvalue of this Hamiltonian and eigenstates.
but i have no idea how to set a coordinate to value the gradient
 

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The electron is fixed in space, hence the spatial part of the quantum state is irrelevant. You only need to concentrate on what happens to the spin.
 
DrClaude said:
The electron is fixed in space, hence the spatial part of the quantum state is irrelevant. You only need to concentrate on what happens to the spin.
upload_2017-9-28_19-8-22.png


This value is always 0 , even though i derivative (wt) by theta or pi
 

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I don't understand why you are invoking eq. (2.6.6) at all. The full Hamiltonian to be considered is given in the problem, and it has no Laplacian operator.
 
DrClaude said:
I don't understand why you are invoking eq. (2.6.6) at all. The full Hamiltonian to be considered is given in the problem, and it has no Laplacian operator.

I think you don't know how to evaluate berry phase, you should look at the last line of relevant equations. There is Dell operator
 
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