Two waves of equal amplitude travel in opposite directions along with the same…

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · Wave mechanics in one dimension

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch The Schrödinger equation and the Born rule

Problem

Two waves of equal amplitude

A

travel in opposite directions along

x

with the same wavenumber

k

and angular frequency

\omega

\Psi(x,t) = Ae^{i(kx-\omega t)} + Ae^{i(-kx-\omega t)}.

((a)) Find

|\Psi(x,t)|^2

, using the complex conjugate, and write it in terms of

\cos(kx)

. ((b)) Say whether

|\Psi|^2

depends on

x

, and contrast this with a single travelling wave

Ae^{i(kx-\omega t)}