A simple model for a quantum particle is the time-independent one-dimensional Schrdinger equation ~ 2 2m d

A simple model for a quantum particle is the time-independent one-dimensional Schrödinger equation

~
2 2m d 2ψ(x)
dx2 = Eψ(x).
Here x represents distance, and ~ is equal to h 2π where h is Planck’s constant. We want to find a function ψ(x) that satisfies this equation. Although we don’t learn in this book how to solve equations like this, we can guess what the solution is, and then check to see if our guess works.
If we guess that ψ(x) = sin(k x), what must k be in order for ψ(x) to be a solution to the one-dimensional Schrödinger equation?