Time-independent Schrödinger equation ↩

Metadata 
shorthands: {}
aliases: [Eigenvector equation of the Schrödinger equation, Stationary Schrödinger equation]
created: 2021-12-11 15:33:48
modified: 2022-01-10 04:13:04

If is the Hamiltonian operator of a quantum system, the eigenvector equation

is called the time-independent Schrödinger equation.

Finding solutions

When solving the equation, we are trying to determine both the numbers (eigenvalues) for which the equation has a nonzero solution and the corresponding vectors (the eigenvectors).

Time evolution of solutions

If is a solution to the time-independent Schrödinger equation with the initial condition , then simply:

Since is just a constant multiple of , we see that represents the same physical state as (due to Axiom 1). Thus, a solution to a time-independent Schrödinger equation is sometimes called a stationary state.