Associated Laguerre functions

Solution of the Schrodinger equation for R i r), known as the radial wave functions since they are functions only of r, follows a well-known mathematical procedure to produce the solutions known as the associated Laguerre functions, of which a few are given in Table 1.2. The radius of the Bohr orbit for n = 1 is given by... 

Hol0ien, E., Phys. Rev. 104, 1301, Radial configurational interaction in He and similar atomic systems." An orthonormal set of associated Laguerre functions is used. 

Hol0IEN, E., Proc. Phys. Soc. A71, 357, "The 2s2 XS state solution of the non-relativistic Schrodinger equation for He and H. " Associated Laguerre functions. 

The im (9) functions are related to the associated Legendre polynomials, and the first few are listed in table 6.1. The R i(r) are the radial wave functions, known as associated Laguerre functions, the first few of which are listed in table 6.2. The quantities n, l and m in (6.8) are known as quantum numbers, and have the following allowed values ... 

These functions are called the associated Laguerre functions. We shall discuss them in detail in succeeding sections. 

In Appendix VII, it is shown that the normalization integral for the associated Laguerre function has the value... 

There is now clear that our radial equation is of Laguerre form with the associate Laguerre function solution through the one-to-one correspondences, solved at once to ... 

This function is called the associated Laguerre function. 

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