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Q5: Apply the Ľ² and Lz operator on the spherical harmonics (wavefunctions) below.
a) (²) cos(0)
b) (2) sin(0) ei
8π
c) (2²) ² sin(
d)
1
√8π
-ip
sin(0)e-
What is the result for each? Which of these functions are eigenfunctions of both operators? What
0, and of course cos e =
дфг
else can you conclude? Hints:
etio
sin 02²
2²
sin 0
etiø
=
sin²0 00²
0.
=

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