Introduction to Quantum Mechanics · Problem 3.44

Formalism — David J. Griffiths

Physics — Quantum Mechanics · three_level_systems

Problem

The Hamiltonian for a certain three-level system is represented by the matrix

\mathsf{H} = \begin{pmatrix} a & 0 & b \\ 0 & c & 0 \\ b & 0 & a \end{pmatrix},

where

a

b

, and

c

are real numbers. (a) If the system starts out in the state

|S(0)\rangle = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix},

what is

|S(t)\rangle

? (b) If the system starts out in the state

|S(0)\rangle = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix},

what is

|S(t)\rangle