Chapter 11, Problem 11.86E

Interpretation Introduction

Interpretation:

The explicit forms of the $2p_{\text{x}}$ and $2p_{\text{y}}$ nonimaginary wavefunctions are to be stated.

Concept introduction:

The wave function for $\text{3-D}$ rotational motion involves spherical polar coordinates to explain the motion in three dimensions. It is given by the expression as follows.

${\Psi }_{m,l}=\frac{1}{\sqrt{2\pi }}{e}^{im\varphi }{\theta }_{l,m_l}$

Where, ${\Psi }_m$ represents the wavefunction dependent on quantum number $m$ and $l$. The values of $m$ and $l$ start from $0$. Also, they can take up both negative and positive integral values. According to Euler’s identity, $e^{im\varphi }$ can be written as $\cos \varphi +i\sin \varphi$.