|
513.001 Molecular and Solid State Physics | |
|
|
EigenfunctionVerify that the $3d_{xy}$ atomic orbital, \[ \begin{equation} \large \phi_{3d_{xy}}=\frac{\sqrt{2}Z^{7/2}}{81\sqrt{\pi}}xye^{-\frac{Zr}{3a_0}}, \end{equation} \]is a normalized eigenfunction of the hydrogen-like-Schrödinger equation, \[ \begin{equation} \large -\frac{\hbar^2}{2m}\nabla^2\phi -\frac{Ze^2}{4\pi\epsilon r}\phi=E\phi. \end{equation} \] |