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Quantum mechanics physics problem

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What is the magnitude of the angular momentum for an l =1 electron? What is the magnitude of the electrons spin angular momentum?

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  1. In quantum mechanics there is angular momentum, and there is angular momentum.

    Operator of angular momentum is vector, its components are

    Lψ = (Lx, Ly, Lz) ψ = (∂/∂φ_x, ∂/∂φ_y, ∂/∂φ_z) ψ,

    where Lx = ∂/∂φ_x is rotation arond x-axis.

    It so happens that neither pair of Li and Lj commute, so a particle can NEVER have definite angular momentum L.

    However operator L²

    L² = ∂²/∂φ_x² + ∂²/∂φ_y² + ∂²/∂φ_z²

    is scalar, it commutes with any component Li and has eigen values

    L(L+1)

    Answer:

    magnitude of the angular momentum for an l =1 electron is

    h√( 1 * (1+1)) = √2 h

    magnitude of the electrons spin 1/2 angular momentum is

    h√( 1/2 * (1/2+1)) =  Ã¢ÂˆÂš3/2 h

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