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

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Homework Help Overview

The discussion revolves around the Berry phase of a spin-1/2 particle in a slowly rotating magnetic field, focusing on the quantum mechanical implications and calculations involved in the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the eigenvalues and eigenstates of the Hamiltonian, with some expressing uncertainty about how to set coordinates for evaluating the gradient. Others emphasize the irrelevance of the spatial part of the quantum state, suggesting a focus on the spin dynamics. There are questions regarding the invocation of specific equations and the absence of certain operators in the Hamiltonian.

Discussion Status

The conversation is ongoing, with participants exploring different interpretations of the problem and questioning the relevance of certain equations. Some guidance has been offered regarding the evaluation of the Berry phase, but no consensus has been reached.

Contextual Notes

There appears to be confusion regarding the Hamiltonian's structure and the necessary operators for the problem, as well as the treatment of the spatial versus spin components of the quantum state.

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Homework Statement


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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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