Chapter 2Laguerre Polynomials

Laguerre polynomials, c02-math-001 are named after the French mathematician Edmond Laguerre (1834–1886). They are the solutions of the Laguerre equation:

2.1 equation

where nonsingular solutions exist only for the non-negative integer values of c02-math-003. 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 equation

can be separated in spherical polar coordinates as c02-math-005 The angular part of the solution, c02-math-006 is the spherical harmonics and the radial part, c02-math-007 comes from the solutions of the differential equation

2.3 equation

Here, is the mass of ...

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