Introductory Quantum Mechanics Liboff 4th Edition Solutions -

The expectation value of the position operator is given by:

−ℏ²/2m (−k²)Ae^(ikx) = E Ae^(ikx)

⟨x⟩ = L/2

: Find the expectation value of the position operator for a particle in a one-dimensional box.

: Using the definitions of the position and momentum operators, we can write: Introductory Quantum Mechanics Liboff 4th Edition Solutions

ℏ²k²/2m = E

[x, p] = iℏ

: Show that the wave function ψ(x) = Ae^(ikx) satisfies the time-independent Schrödinger equation for a free particle.