In my book it states the magnetic quantum number “$m_\ell$" is the spatial orientation of the orbital with respect to a standard set of coordinates. I get what $n$ and $\ell$ is, but what does it mean visually or conceptually, if $m_\ell$ is $1$ vs $-1$? For instance if $n = 4$, $\ell = 1$ and $m_\ell = -1$ vs. $n = 4$, $\ell = 1$ and $m_\ell = 1$?
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