Formula: Angular Momentum of a Quantum Particle Magnetic quantum number
$$L_{\text z} ~=~ \class{violet}{m} \, \hbar$$
$$L_{\text z} ~=~ \class{violet}{m} \, \hbar$$
$$\class{violet}{m} ~=~ \frac{ L_{\text z} }{ \hbar }$$
Angular momentum component
$$ L_{\text z} $$ Unit $$ \mathrm{Js} $$
This is one of the three components of the total orbital angular momentum \(\boldsymbol{L} = [ L_{\text x},~ L_{\text y},~ L_{\text z} ] \) of an electron in an atom (e.g. H-atom). The \(L_{\text z}\) component is quantized and occurs only as a multiple of the Planck's constant \(\hbar\).
Magnetic quantum number
$$ \class{violet}{m} $$ Unit $$ - $$
The magnetic quantum number indicates how large the \(L_{\text z}\) component of the orbital angular momentum is. For the orbital angular momentum quantum number \( l = 2 \) the magnetic quantum number can take on the values -2, -1, 0, 1 and 2.
Reduced Planck's constant
$$ \hbar $$ Unit $$ \mathrm{Js} = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{s} } $$
Reduced quantum of action is a physical constant that often appears in the equations of quantum mechanics. It has the value: \( \hbar ~=~ \frac{h}{2 \pi} ~=~ 1.054 \, 572 ~\cdot~ 10^{-34} \, \text{Js} \).