Chapter 11, Problem 11.65E

Interpretation Introduction

Interpretation:

The validation of the statement that for constant $r$ and $V=0$, equation 11.56 becomes equation 11.46 is to be stated.

Concept introduction:

Rigid rotor is a system in which more than one particle has fixed relative positions and it rotates in the three dimensional space.

The Schrödinger equation in three dimensional space is given by,

$\left\{\frac{-{\hslash }^2}{2\mu }\left[\frac{1}{r^2}\frac{\partial }{\partial r}\left(r^2\frac{\partial }{\partial r}\right)+\frac{1}{r^2\sin \theta }\frac{\partial }{\partial \theta }\left(\sin \theta \frac{\partial }{\partial \theta }\right)+\frac{1}{r^2{\sin }^2\theta }\frac{{\partial }^2}{\partial {\varphi }^2}\right]+\widehat{V}\right\}\Psi =E\Psi$

The spherical polar coordinates are $\theta$, $\varphi$ and r.