A Modern Approach to Quantum Mechanics · Problem 9.21

Bound States of Central Potentials — John S. Townsend

Physics — Quantum Mechanics · rigid-rotator-magnetic-field

Problem

Suppose that the rigid rotator of Problem 9.20 is immersed in a uniform magnetic field B=B0k\mathbf{B} = B_0\mathbf{k}, and that the Hamiltonian is given by H^=L^22I+ω0L^z\hat{H} = \frac{\hat{L}^2}{2I} + \omega_0\hat{L}_z where ω0\omega_0 is a constant. If ⟨θ,ϕ∣ψ(0)⟩=34πsin⁡θsin⁡ϕ\langle\theta, \phi|\psi(0)\rangle = \sqrt{\frac{3}{4\pi}}\sin\theta\sin\phi what is ⟨θ,ϕ∣ψ(t)⟩\langle\theta, \phi|\psi(t)\rangle? What is ⟨Lx⟩\langle L_x\rangle at time tt?

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