What are the magnetic quantum numbers for specific d orbitals? I mean I know they’re $\ce{d_{-2}}$, $\ce{d_{-1}}$, $\ce{d_{0}}$, $\ce{d_{1}}$, $\ce{d_{2}}$ but how do these numbers relate to each one of $\ce{d}$ orbitals $\ce{d_{z_2}}$, $\ce{d_{xz}}$, $\ce{d_{yz}}$, $\ce{d_{xy}}$, $\ce{d_{x_2 - y_2}}$)?
I couldn't find a definitive answer anywhere.
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*}