# Compute the Following for Orbital Angular Momentum

**Question description**

1.Expand a general function ψ(r, θ, φ) in terms of spherical harmonics. What do expansion coefficients represent in terms of probabilites? i.At a given r, if we measure only L^2, what is the probability to find the result l(l+1)?What is the total probability(for all r) ? ii.At a given r, if we measure only Lz, what is the probability to find the result m? What is the total probability(for all r) ? iii.If we consider ψ(r, θ, φ) as a function of φ defined on [0, 2π] and depending on parameters r, θ, we can expand it as a fourier series. What are the expansion coefficients? What is the total probability to find Lz value equal to m?

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