The $\mathrm{m_l}$ values in quantum mechanics, $1, 0, -1$ for p orbitals for example, do they refer to specific orbitals? Like, does $\mathrm{m_l} = 1$ refer specifically to $\mathrm{p_x, m_l} = 0$ refers to $\mathrm{p_y}$, and $\mathrm{m_l} = -1$ refer to $\mathrm{p_z}$? Or are these values arbitrarily defined?

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    $\begingroup$ They are not arbitrary, nor do they refer to specific orbitals one to one. Indeed, $m_l=0$ for $p_z$; now, $p_x$ and $p_y$ are the linear combinations of the orbitals with $m_l=\pm1$. $\endgroup$ – Ivan Neretin Apr 13 at 2:27

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