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

[BREAD]

Homework Statement

Homework Equations

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

The Attempt at a Solution

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

 

[DrClaude]

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.

 

[BREAD]

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.

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

 

[DrClaude]

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.

 

[BREAD]

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