(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An electron is inside a magnetic field oriented in the z-direction. No measurement of the electron has been made. A magnetic field in the x-direction is now switched on. Calculate the first-order change in the energy levels as a result of this perturbation.

3. The attempt at a solution

I got this wrong, claiming that the first order perturbation is zero. I said this because if you evaluate the expectation of the [itex]S_x[/itex] matrix in the states up/down individually, you obviously get zero since [itex]S_x[/itex] is anti-diagonal.

Apparently you are supposed to evaluate the expectation of [itex]S_x[/itex] in the superposition of states [itex]\psi = 1/\sqrt{2}(1,0)^T + 1/\sqrt{2}(0,1)^T[/itex]. I have trouble understanding this because [itex]\psi[/itex] is not an eigenstate of the orginial Hamiltonian, which it should be for canonical perturbation theory.

Any help is greatly appreciated.

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# Homework Help: Canonical perturbation theory

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