Energy eigenstates

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

$\hat{H}\Psi_n=E_n\Psi_n$

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

Ψ

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 is also time-independent.

See also: Energy eigenstates, Eigenvalues, Eigenvector, Eigenvectors, Hamiltonian, Quantum mechanics, Schroedinger equation