Energy eigenstates

The Energy eigenstates of a quantum system are the set of eigenvalues and eigenvectors obtained by solving the time-independent Schrödinger equation for the system in question,

${\hat {H}}\Psi _{n}=E_{n}\Psi _{n}$

where ${\hat {H}}$ is the time-independent Hamiltonian operator,

$\Psi$ is the nth energy eigenvector (also known as eigenfunction or wavefunction),

and $E_{n}$ is the nth energy eigenvalue.

In the case of a system with a time-independent Hamiltonian operator, this set of eigenvalues are also called stationary states, because they are time-independent.