A Modern Approach to Quantum Mechanics · Problem 11.6

Identical Particles — John S. Townsend

Physics — Quantum Mechanics · spin-half-magnetic-field-perturbation

Problem

The spin Hamiltonian for a spin-12\frac{1}{2} particle in an external magnetic field is H^=−μ^⋅B=−gq2mcS^⋅B\hat{H} = -\hat{\mu}\cdot\mathbf{B} = -\frac{gq}{2mc}\hat{\mathbf{S}}\cdot\mathbf{B} Take B=B0k+B2j\mathbf{B} = B_0\mathbf{k} + B_2\mathbf{j}, with B2≪B0B_2 \ll B_0. Determine the energy eigenvalues exactly and compare with the results of perturbation theory through second order in B2/B0B_2/B_0.

Related theory

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