A Modern Approach to Quantum Mechanics · Problem 4.13

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

Physics — Quantum Mechanics · three-state-hamiltonian-time-evolution

Problem

Let (E00A0E10A0E0)\begin{pmatrix} E_0 & 0 & A \\ 0 & E_1 & 0 \\ A & 0 & E_0 \end{pmatrix} be the matrix representation of the Hamiltonian for a three-state system with basis states ∣1⟩|1\rangle, ∣2⟩|2\rangle, and ∣3⟩|3\rangle. (a) If the state of the system at time t=0t = 0 is ∣ψ(0)⟩=∣2⟩|\psi(0)\rangle = |2\rangle, what is ∣ψ(t)⟩|\psi(t)\rangle? (b) If the state of the system at time t=0t = 0 is ∣ψ(0)⟩=∣3⟩|\psi(0)\rangle = |3\rangle, what is ∣ψ(t)⟩|\psi(t)\rangle?

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