Formula: Angular Momentum of a Quantum Particle Magnetic quantum number   

Formula: Angular Momentum of a Quantum Particle
Quantized Lz Component of the Angular Momentum
Lz of the Quantum Mechanical Angular Momentum Precisely Determined But Lx and Ly Not

Angular momentum component

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

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

Reduced quantum of action is a physical constant that often appears in the equations of quantum mechanics. It has the value: \( \hbar ~=~ \frac{h}{2 \pi} ~=~ 1.054 \, 572 ~\cdot~ 10^{-34} \, \text{Js} \).

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