A Modern Approach to Quantum Mechanics · Problem 12.8

Scattering — John S. Townsend

Physics — Quantum Mechanics · variational-method-3d-harmonic-oscillator

Problem

Use the trial wave function

R(r) = Ne^{-br}

to estimate the ground-state energy of the three-dimensional isotropic harmonic oscillator, for which

V(r) = \frac{1}{2}\mu\omega^2 r^2

. Compare your estimate with the exact value (see Section 10.5).