Principles of Quantum Mechanics · Problem 21.1

Path Integrals—II — R. Shankar

Physics — Quantum Mechanics · path-integrals

Problem

Verify Equation 21.20 by showing that if

\Psi(x, t_0)

is normalized, then so is

\Psi(x, t)

for all

t > t_0

. Hint: Use the fact that

G(x, x'; t, t_0)

satisfies the Schrödinger equation in

x

and

t

, and its complex conjugate satisfies it in

x'

and

t_0