An electron of mass moves in a harmonic potential of angular frequency and occupies…
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Wave mechanics in one dimension · Wave mechanics in one dimension
The Structure of Quantum Mechanics, Ch The oscillator as an algebra
Problem
An electron of mass m=9.11×10−31kg moves in a harmonic potential of angular frequency ω=1.5×1015rads−1 and occupies the number state ∣n=4⟩.
((a)) Using p^=iℏmω/2(a^†−a^), obtain ⟨n∣p^2∣n⟩ by counting which terms survive.
((b)) Evaluate it for n=4.