A Modern Approach to Quantum Mechanics · Problem 4.10

A System of Two Spin-1/2 Particles — John S. Townsend

Physics — Quantum Mechanics · ammonia-molecule-hamiltonian-basis-change

Problem

Express the Hamiltonian (4.57) for the ammonia molecule in the ∣I⟩|I\rangle-∣II⟩|II\rangle basis to obtain (4.61). Assume the electric field E=E0cos⁡ωt\mathbf{E} = \mathbf{E}_0 \cos\omega t. Compare this Hamiltonian with that for a spin-12\frac{1}{2} particle in a time-dependent magnetic field that appears in (4.38) and deduce the form for the probability of finding the molecule in state ∣I⟩|I\rangle at time tt if it is initially placed in the state ∣II⟩|II\rangle; that is, what is the analogue of Rabi's formula (4.45) for the ammonia molecule?

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