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## Homework Statement

A particle in a spherically symmetric potential is in a state described by the wavepacked

[tex] \psi (x,y,z) = C (xy+yz+zx)e^{-alpha r^2} [/tex]

What is the probability that a measurement of the square of the angular mometum yields zero?

What is the probability that it yields [tex] 6\hbar^2 [/itex]?

If the value of l is found to be 2. what are the relative probabilities of m=-2,-1,0,1,2

**2. The attempt at a solution**

i think the first part is simply aking to calculate [itex] <L^2>[/itex]

but the carteisna coords are throwing me off... Should i convert to spherical polars?? Till now whenever the angular momentum L^2 and Lz were required, they were gotten using

[tex] \hat{L^2} \psi_{nlm_{l}} = l(l+1) \psi_{nlm_{l}} [/tex]

really from the spherical harmonics... however conversion to spherical polars doesnt yield any familiar spherical harmonic either.

can it written in a way that yields familiar spherical harmonics, however??