Chapter 11, Problem 11.9E

Interpretation Introduction

Interpretation:

The given statement that the second derivative of $\Psi$ given by equation 11.8 gives equation 11.9 is to be verified.

Concept introduction:

The Schrödinger equation for one-dimensional harmonic oscillator is,

$\left[-\frac{{\hslash }^2}{2m}\frac{d^2}{d{x}^2}+2{\pi }^2{v}^{2}m{x}^2\right]\Psi =E\Psi$

Where,

• $v$ is the frequency.

• $m$ is the mass of the body.

• $\Psi$ is the wavefunction of harmonic oscillator.

• $E$ is the energy of harmonic oscillator.

• $\hslash$ has the value $\frac{h}{2\pi }$