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Prove (a) that ψ ± = N (x ± iy)f(r) is an eigenfunction of L^2 and...

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Physics

Prove
(a) that ψ ± = N (x ± iy)f(r) is an eigenfunction of L^2 and Lz andset the eigenvalues corresponding.
(b) Construct a wave function ψ_0(r) that is an eigenfunction of L^2whose eigenvalue is the same as that of a), but whose eigenvalue Lzdiffers by a unit of the one found in a).
(c) Find an eigenfunction of L^2 and Lx, analogous to those ofparts a) and b), which have the same eigenvalue L^2 but whoseeigenvalue Lx is maximum
(d) If the wave function for a particle is that of part c), whatare the probabilities of finding it in each of the states describedby the wave functions ψ0, ψ + and ψ− of a) and b)?

thank you so much

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