Question #6562

Find the probability distributions of the orbital angular momentum

variables L2 and Lz for the following orbital state functions:

(a) Ψ(x) = f(r) sinθ cos φ,

(b) Ψ(x) = f(r)(cos θ)^2,

(c) Ψ(x) = f(r) sinθ cos θ sin φ.

Here r, θ, φ are the usual spherical coordinates, and f(r) is an arbitrary

radial function (not necessarily the same in each case) into which the

normalization constant has been absorbed.

variables L2 and Lz for the following orbital state functions:

(a) Ψ(x) = f(r) sinθ cos φ,

(b) Ψ(x) = f(r)(cos θ)^2,

(c) Ψ(x) = f(r) sinθ cos θ sin φ.

Here r, θ, φ are the usual spherical coordinates, and f(r) is an arbitrary

radial function (not necessarily the same in each case) into which the

normalization constant has been absorbed.

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