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Angular momentum in QM
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Quantised magnitude and projection.
L = √(l(l+1))ħThe magnitude L = √(l(l+1))ħ and one component L_z = mħ are quantised. The other components remain uncertain.
l = 1: L = 1.41ħ, L_z ∈ {−ħ, 0, ħ}.
L never equals lħ exactly.
In more detail
Angular momentum in quantum mechanics is quantised, with magnitude sqrt(l(l+1))ħ and z-component m_l ħ. Its operators follow specific commutation relations.
Real-world uses
- Atomic spectra depend on quantised angular momentum.
- Nuclear physics uses angular momentum to classify states.
- Chemists use the angular momentum quantum numbers to predict the shapes and energies of atomic orbitals.
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Frequently asked questions
Can angular momentum be measured exactly?
Only one component at a time, due to the commutation relations.
Is l always an integer?
For orbital angular momentum, yes. Spin can be a half-integer.
Why is the magnitude given as a square root?
The quantised angular momentum has length square root of l times l plus one, times the reduced Planck constant.
Related topics in Quantum Mechanics
Pauli exclusion principle · Fermions and bosons · Identical particles · Addition of angular momenta · Spin–orbit coupling · Zeeman effect