A Modern Approach to Quantum Mechanics · Problem 11.10

Identical Particles — John S. Townsend

Physics — Quantum Mechanics · spin-1-crystal-hamiltonian-perturbation

Problem

The spin Hamiltonian of a spin-1 ion in a crystal is given by H^=aℏ2S^z2+bℏ2(S^x2−S^y2)\hat{H} = \frac{a}{\hbar^2}\hat{S}_z^2 + \frac{b}{\hbar^2}(\hat{S}_x^2 - \hat{S}_y^2) Assume b≪ab \ll a and treat bℏ2(S^x2−S^y2)\frac{b}{\hbar^2}(\hat{S}_x^2 - \hat{S}_y^2) as a perturbation. Calculate the unperturbed energies and the first-order corrections using perturbation theory. Beware of the degeneracy. Compare your perturbative results with the exact eigenvalues.

Related theory

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