Special Mathematical Functions
Hermite polynomials
Note
What? Solution of the 1D Harmonic Oscillator
Wave-function:
where
Recursion relation:
(
)

Spherical harmonics
Note
What? Solution of the angular part of the Schrödinger equation of a central potential
Where? Chapter 9: Translational and Rotational Symmetry in the Two-Body Problem
Wave-function:
The first few solutions are:

Legendre Polynomial
To be added in future update
Laguerre Polynomial
To be added in future update