Past exam of the physics A course of the University of Cambridge / 2010 / Paper 2 / Section A / 2 / Solution

For normalized amplitudes $c_n,c_{n^{\prime }}$ and a time-independent observable $A$, the Schrödinger equation givesThe interference term therefore hasThis is the period of two-state quantum interference. If the off-diagonal matrix element or either amplitude vanishes, the expectation value is constant, so this is not its unique fundamental period. Equal energies likewise give no beat.