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1. Write the general equation for the spherical harmonic Y,'(0, $) and identify Om($), P;" (cos 0), and the normalization constant. 2. Show that Y,' (0,¢) is an eigenfunction of L'. What is the eigenvalue? 3. Show that Y(0,$) and Y,' (0,¢) are orthogonal.

1. Write the general equation for the spherical harmonic Y,'(0, $) and identify Om($), P;" (cos 0), and the normalization constant. 2. Show that Y,' (0,¢) is an eigenfunction of L'. What is the eigenvalue? 3. Show that Y(0,$) and Y,' (0,¢) are orthogonal.

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|m| 1. Write the general equation for the spherical harmonic Y; (0, p) and identify Om(), P' (cos 0), and the normalization constant. 2. Show that Y, (0, $) is an eigenfunction of L². What is the eigenvalue? 3. Show that Y (0,¢) and Y†'(0, p) are orthogonal.
Transcribed Image Text:|m| 1. Write the general equation for the spherical harmonic Y; (0, p) and identify Om(), P' (cos 0), and the normalization constant. 2. Show that Y, (0, $) is an eigenfunction of L². What is the eigenvalue? 3. Show that Y (0,¢) and Y†'(0, p) are orthogonal.
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