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(Solved): 16. A particle in a spherically symmetrical potential is known to be in an eigenstate of L2 and Lz ...
16. A particle in a spherically symmetrical potential is known to be in an eigenstate of L2 and Lz with eigenvalues ℏ2l(l+1) and mℏ, respectively. Prove that the expectation values between ∣lm⟩ states satisfy ⟨Lx⟩=⟨Ly⟩=0,⟨Lx2⟩=⟨Ly2⟩=2[l(l+1)ℏ2−m2ℏ2].
the eigenvalues of and is given i.e. also to calculate eigenvalues of , there will be a requirement of a ladder operator i.e. given as and there eigenvalues aresimilarly,