Chapter 11, Problem 11.43E

Interpretation Introduction

Interpretation:

The first four $\text{2-D}$ rotational wave functions in terms of sine and cosine using Euler’s identity are to be stated.

Concept introduction:

The wave function for $\text{2-D}$ rotational motion is given below.

${\Psi }_m=\frac{1}{\sqrt{2\pi }}{e}^{im\varphi }$

Where, ${\Psi }_m$represents the wave function dependent on quantum number $m$. The values of $m$ start from $0$. Also, it can take up both negative and positive integral values.

According to Euler’s identity, $e^{im\varphi }$ can be written as $\cos \varphi +i\sin \varphi$.