4th Edition Solutions: Introductory Quantum Mechanics Liboff

[x, p] = iℏ

ψn(x) = √(2/L) sin(nπx/L)

: Show that the wave function ψ(x) = Ae^(ikx) satisfies the time-independent Schrödinger equation for a free particle. Introductory Quantum Mechanics Liboff 4th Edition Solutions

⟨x⟩ = L/2

Substituting ψ(x) = Ae^(ikx) into the equation, we get: [x, p] = iℏ ψn(x) = √(2/L) sin(nπx/L)