# Quantum harmonic oscillator

We get the time-independent Schrödinger equation by substituting this into Equation "time-independent Schrödinger equation for a one dimensional particle": $$[−2mℏ​∂x∂2​+x2]ψ=Eψ(x) (1)$$
The first is the stupid "here's a guess" + "hey this family of solutions forms a complete bases"! This is exactly how we solved the problem at Section "Solving partial differential equations with the Fourier series", except that now the complete basis are the Hermite functions.
The second is the much celebrated ladder operator method.

## Quantum LC circuit

A quantum version of the LC circuit!
TODO are there experiments, or just theoretical?

## Hermite polynomials

I.e.: they are both:

## Hermite functions

Not the same as Hermite polynomials.