The Hamiltonianof a particle of mass μ in a spherically symmetric potential:
H=2μp2+V(r) Angular momentum operators:
Lz=−iℏ(x∂y∂−y∂x∂),L2=Lx2+Ly2+Lz2 Angular momentum in spherical coordinates:
Lz=−iℏ∂ϕ∂,L2=−ℏ2(sinθ1∂θ∂(sinθ∂θ∂)+sin2θ1∂ϕ2∂2) As the hamiltonian is independent of θ,ϕ coordinates,
[Lz,H]=0,[L2,H]=0
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