This is taken from a text problem, but I am putting it in this section because I think my question goes beyond the problem itself:(adsbygoogle = window.adsbygoogle || []).push({});

If a particle has a wave function psi = A*R(r)*cos^{2}(theta), for example, then if I want to find the probability that its angular momentum is l I would find the absolute value squared of

P(l) = <L=l|psi> .

But the eigenstates of the angular momentum operator are products of exp(i*l*theta/h) and an unspecified function of r. If I do the above integral, don't I have to know what the function of r in the eigenfunction for L is? (I mean L_{z}, to be precise).

This got me thinking--in this case, |psi> is a tensor product of kets from two Hilbert Spaces, a space with elements depending on r only and a space with elements depending on theta only, correct?

When such a product is put into the r, theta basis, the resulting wave function is a product of a function of r and a function of theta. So does this mean that all wave functions are like this, i.e. products of functions of one variable? In other words, it would be impossible to have a wave function like exp(i*r*theta), for instance? (Aside from the normalization problem)

Thanks for your time.

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# Angular Momentum eigenstates, and tensor products

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