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The spherical harmonics wavefunction Y,²(0, 4) = sin²0 e¬i2 is given.
a) Normalize the wavefunction.
b) Show that Y7²(0, 4) is an eigenfunction of the total energy operator ( Hamiltonian) for 3D
rigid rotator model
c) What is the energy and the degeneracy of the state represented by Yz²(0, 4)?

h= 6.626x1034 J.s c=2.998x10% m.s1 1 eV = 1.6022x10-19 J 1Å = 10-10 m,
%3D
x*e-ax² dx = O" sin e de =
1/2
S" sin50
6
16
mẹ =9.109x10-31 kg, k= 1.3807x10-23 J/K
8a2
15

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