Q5: Apply the Ľ² and Lz operator on the spherical harmonics (wavefunctions) below. a) (2) Cos b) cos(0) (2) sin(0) ei d) T sin(0)e-ip What is the result for each? Which of these functions are eigenfunctions of both operators? What etio sin Ꮎ Ꭷ2 etip sin20 дф2 = 0, and of course cos 0 = 0. 2² a0² else can you conclude? Hints: = 0. sin 0
Q5: Apply the Ľ² and Lz operator on the spherical harmonics (wavefunctions) below. a) (2) Cos b) cos(0) (2) sin(0) ei d) T sin(0)e-ip What is the result for each? Which of these functions are eigenfunctions of both operators? What etio sin Ꮎ Ꭷ2 etip sin20 дф2 = 0, and of course cos 0 = 0. 2² a0² else can you conclude? Hints: = 0. sin 0
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Transcribed Image Text: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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