Introduction to Quantum Mechanics · Problem 3.38

Formalism — David J. Griffiths

Physics — Quantum Mechanics · energy_time_uncertainty

Problem

In an interesting version of the energy-time uncertainty principle Δt=τ/π\Delta t = \tau/\pi, where τ\tau is the time it takes Ψ(x,t)\Psi(x, t) to evolve into a state orthogonal to Ψ(x,0)\Psi(x, 0). Test this out, using a wave function that is a linear combination of two (orthonormal) stationary states of some (arbitrary) potential: Ψ(x,0)=(1/2)[ψ1(x)+ψ2(x)]\Psi(x, 0) = \left(1/\sqrt{2}\right)[\psi_1(x) + \psi_2(x)].

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