The normalized wavefunction of a particle in three dimensions is given by
ψ(x, y, z) = N z exp[−a(x2 + y2 + z2)]
where a is a positive constant and N is a normalization constant. If L is the angular momentum operator, the eigenvalues of L2 and Lz, respectively, are
1
2h2 and h
2
h2 and 0
3
2h2 and 0
4
\(\frac{{\rm{3}}}{{\rm{4}}}{{\rm{h}}^{\rm{2}}}\,{\rm{and}}\,\frac{1}{2}{\rm{h}}\)
5
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