More generally, one can consider a system where the two levels under consideration are not energy eigenstates.

The solutions are energy eigenstate of the system.

For quantum mechanical systems with discrete energy eigenstates, a similar theorem holds.

These relations can be used to find the energy eigenstates of the quantum harmonic oscillator.

Suppose that two or more energy eigenstates are degenerate.

In many systems, two or more energy eigenstates have the same energy.

The generalized force for a system known to be in energy eigenstate is given by:

The number of energy eigenstates that move from below to above is, of course, given by .

The band structure is the collection of energy eigenstates within the first Brillouin zone.

The former proves that the Bloch waves are energy eigenstates.