Show up in the solution of the quantum harmonic oscillator after separation of variables leading into the time-independent Schrödinger equation, much like solving partial differential equations with the Fourier series.
I.e.: they are both:
- solutions to the time-independent Schrödinger equation for the quantum harmonic oscillator
- a complete basis of that space
Not the same as Hermite polynomials.
Articles by others on the same topic
Hermite polynomials are a set of orthogonal polynomials that arise in probability, combinatorics, and physics, particularly in the context of quantum mechanics and the study of harmonic oscillators. They are defined by a specific recurrence relation and can be generated using generating functions.