Question
The complex forms for the spherical harmonics with l=3 and ml= +3 and -3 are: Y33...
The complex forms for the spherical harmonics with l=3 and ml= +3 and -3 are:
Y33 =
Nsin3θei3φ and
Y3-3 =
Nsin3θe-i3φ. Using the
Euler expansion on the negative exponentials, show how the linear
combination Y33+
Y3-3results in a real function, and
the linear combination
–i(Y33-
Y3-3) result in a
different real function. Are these real functions orthogonal to
each other? Explain
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