2. In this problem, we'll take a closer look at the "spherical harmonics", aka the solutions to the rigid rotor. Specifically, we'll look into the different "nodes" present in each wavefunction-i.e. places where Y, = 0. For cach wavefunction given, determine the values of 0 and o where nodes occur. For each wavefunction, briefly discuss and/or sketch: what do these nodes look like in 3D? Does the # of nodes you found match what you would expect based on your knowledge of "orbitals"? a. Y (0, 4) = %3D b. Y (0,) = cos e c. Y (0, ) = sin 0 e
2. In this problem, we'll take a closer look at the "spherical harmonics", aka the solutions to the rigid rotor. Specifically, we'll look into the different "nodes" present in each wavefunction-i.e. places where Y, = 0. For cach wavefunction given, determine the values of 0 and o where nodes occur. For each wavefunction, briefly discuss and/or sketch: what do these nodes look like in 3D? Does the # of nodes you found match what you would expect based on your knowledge of "orbitals"? a. Y (0, 4) = %3D b. Y (0,) = cos e c. Y (0, ) = sin 0 e
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Transcribed Image Text:2. In this problem, we'll take a closer look at the "spherical harmonics", aka the solutions to the
rigid rotor. Specifically, we'll look into the different "nodes" present in each wavefunction-i.c.
places where Y, = 0. For cach wavefunction given, determine the values of 0 and o where
nodes occur. For each wavefunction, briefly discuss and/or sketch: what do these nodes look like
in 3D? Does the # of nodes you found match what you would expect based on your knowledge
of "orbitals"?
a. Y (0, 4) =
b. Y (0,) =
3
cos e
%3D
c. Y (0,) =
3
sin 0 e
15
d. Y (0, 4) =
sin 0 cos 0 e'
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