A **stationary state** is described by a wavefunction that is associated with a probability density and an expectation value that are both independent of time.

For the time-independent Schrodinger equation, , its solutions are stationary states. This implies that stationary states of the time-independent can be represented by basis wavefunctions but not linear combinations of basis wavefunctions with non-zero coefficients. For example, the wavefunction describes a stationary state because:

and

whereas does not describe a stationary state because:

where the last two terms of the RHS of the last equality are time-dependent.

If and describe a degenerate state, where , then describes a stationary state. Since an observable of a stationary state, e.g. , is independent of time, every measurement of of systems in such a state results in the same value .