Mathematical Methods in Science and Engineering, 2nd Edition

Chapter 2Laguerre Polynomials

Laguerre polynomials, are named after the French mathematician Edmond Laguerre (1834–1886). They are the solutions of the Laguerre equation:

2.1

where nonsingular solutions exist only for the non-negative integer values of . We encounter them in quantum mechanics in the solutions of the hydrogen atom problem.

2.1 Central Force Problems in Quantum Mechanics

For the central force problems solutions of the time-independent Schrödinger equation:

2.2

can be separated in spherical polar coordinates as The angular part of the solution, is the spherical harmonics and the radial part, comes from the solutions of the differential equation

2.3

Here, is the mass of ...