Selection Rules and Intensities for Surface-harmonic Wave Functions

Selection Rules and Intensities for Surface-harmonic Wave Functions.—In Section 18 we showed that the wave functions for a system of two particles interacting with one another in the way corresponding to the potential function 

1 This statement is true only to within the degree of approximation of our treatment. A more complete discussion shows that transitions may also occur as a result of interactions corresponding to quadrupole terms and still higher terms, as mentioned in Section 3, and as a result of magnetic interactions. 

The components of electric dipole moment along the x, y, and z axes are 

Let us first discuss the light polarized along the z axis, corresponding to the dipole moment y,. From the orthogonality 

A similar treatment of the integrals for x and y shows that light polarized along these axes is emitted only when m changes by +1 or —1, and 1 changes by +1 or —1. 

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