Radial Recurrence Relations

Dong Shi-Hay, M. Lozada-Cassou, Generalized hypervirial and recurrence relations for radial matrix elements in arbitrary dimensions, Modern Phys. Lett. A 20 (20) (2005) 1533-1540. 

If and Cj, are the cartesian components of e , then, as explained in the previous section, the linear combinations of 4 and 4 f forming e i or are obtained by comparison with the x- and y-components of the Tree-space field e, - of Table 25-2. Using Eq. (37-49) to transform the radial and azimuthal components, and the recurrence relations of Eq. (37-72) for the Bessel functions, we obtain the combinations for even tfnd odd ITE and ITM modes in Table 25-4. The method of construction ensures that these modes have the same normalization as the Tree-space modes and the exact radiation modes of Table 25-3. 

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