Stationary state

A stationary state is a quantum state in which all observables are independent of time. Stationary states are eigenstates of the Hamiltonian operator. For this reason, they are often referred to as energy eigenstates or energy eigenkets.

Stationary states are solutions to the time-independent Schrödinger equation

where $\hat{H}$ is the Hamiltonian operator, $|\Psi\rangle$ is the system's state, and $E$ is the energy eigenvalue associated with the stationary state.

:::image(sidebar) The first two graphs show stationary states of the quantum harmonic oscillator (ground state and first excited state), while the third is a linear combination of the first two states: $\psi_{N}=(\psi_{0}+\psi_{1})/\sqrt{2}$. The orange and blue components are the real and imaginary parts of the wave function, respectively. From Wikipedia. :::