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Okay, if I want to do a Fourier Analysis of a wavefunction, I can use the following transform pairs for real space and momentum space.

Ψ(x) = (2π hbar)^(-1/2) * ∫ dp Φ(p) exp(ipx/hbar)

Φ(p) = (2π hbar)^(-1/2) * ∫ dx Ψ(x) exp(-ipx/hbar)

So, what I want to know is what is the appropriate transform pair for angular momentum.

Let's say that our real space wavefunction is expressed in terms of cylindrical coordinates, and we are only concerned with the angular term Ψ(θ).

Do we want to transform this into angular momentum space? Is this expression correct?

Ψ(θ) = (2π hbar)^(-1/2) * ∫ dL Φ(L) exp(iLθ/hbar)

eNtRopY

Ψ(x) = (2π hbar)^(-1/2) * ∫ dp Φ(p) exp(ipx/hbar)

Φ(p) = (2π hbar)^(-1/2) * ∫ dx Ψ(x) exp(-ipx/hbar)

So, what I want to know is what is the appropriate transform pair for angular momentum.

Let's say that our real space wavefunction is expressed in terms of cylindrical coordinates, and we are only concerned with the angular term Ψ(θ).

Do we want to transform this into angular momentum space? Is this expression correct?

Ψ(θ) = (2π hbar)^(-1/2) * ∫ dL Φ(L) exp(iLθ/hbar)

eNtRopY

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