Introduction to Quantum Mechanics · Problem 8.2

The Variational Principle — David J. Griffiths

Physics — Quantum Mechanics · variational_principle_bounds

Problem

Find the best bound on

E_{\text{gs}}

for the one-dimensional harmonic oscillator using a trial wave function of the form

\psi(x) = \frac{A}{x^2 + b^2},

where

A

is determined by normalization and

b

is an adjustable parameter.