What are the magnetic quantum numbers for specific d orbitals?
On p. 238 of my copy of McQuarrie (1983; his Table 6-6), he lists the following for the hydrogenlike atomic wave functions (expressed as real functions), describing these as "commonly used":
\begin{align*}
n=3, l = 2, m=0:     &amp; \ \psi_{3d_{z^2}} \ ... \\
n=3, l = 2, m=\pm 1: &amp; \ \psi_{3d_{xz }} \ ... \\
       : &amp; \ \psi_{3d_{yz }} \ ... \\
n=3, l = 2, m=\pm 2: &amp; \ \psi_{3d_{x^2-y^2 }} \ ... \\
       : &amp; \ \psi_{3d_{xy }} \ ... \\
\end{align*}