Emission and absorption of radiation Raman

A computation of Raman intensities can be done precisely in the same way as for infrared intensities. One needs here, in addition to the wave functions of the initial and final state, the polarizability tensor a(r,0, )). This is a symmetric tensor of rank 2 that in Cartesian coordinates can be written as 

It has six independent components. It is convenient to separate the trace of this tensor from the rest and thus introduce spherical tensors 

The expressions of the Sections 1.5 and 1.6 are general and apply to any solution of the Schrodinger equation. In the special case of a Morse potential, the radial integrals in Eq. (1.34) can be evaluated, with some approximations, in closed form. The approximation consists in replacing the lower limit of integration by -oo. This approximation is similar to that used in Section 1.3 when obtaining the wave functions. Thus 

Three types of matrix elements have been evaluated.3 (a) M(r) = 

In comparing the algebraic and differential approach in Chapter 2 it will turn out to be useful to consider also the case of two dimensions. Introducing polar coordinates in the plane, 

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