Formula: Angular Momentum / Spin of a Quantum Particle Angular momentum quantum number    Planck's Constant

Formula: Angular Momentum / Spin 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

Unit
Amount of angular momentum of a quantum mechanical particle (for example, an electron).
  • Orbital angular momentum quantum numbers: l= 0, 1, 2, ...
  • Spin quantum numbers: l = 1/2, 3/2, 5/2, ...

Angular momentum quantum number

Unit
The angular momentum quantum number accepts non-negative numbers in +1 steps: \( l \in \left\{ 0, \, \frac{1}{2}, \, 1, \, \frac{3}{2}, \, 2,~... \right\} \)

Reduced Planck's constant

Unit
Reduced Planck's constant 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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