A Modern Approach to Quantum Mechanics · Problem 7.12

Path Integrals — John S. Townsend

Physics — Quantum Mechanics · harmonic-oscillator-gaussian-eigenfunction

Problem

Substitute

\psi(x) = Ne^{-ax^2}

into the position-space energy eigenvalue equation (7.95) and determine the value of the constant

a

that makes this function an eigenfunction. What is the corresponding energy eigenvalue?