Stationary state

Summary

A stationary state is a quantum state that does not change under time evolution, apart from an overall phase of its state vector. The stationary states are the eigenvectors of the Hamiltonian, and the eigenvalue is the energy of the state. Finding them means solving the time-independent Schrödinger equation $H\psi = E\psi$. All measurement probabilities in a stationary state are constant in time. The energies of the stationary states of an atom are its energy levels, and the differences between them give its spectral lines.