Page "Degenerate energy levels" Paragraph 0

In physics, two or more different quantum states are said to be degenerate if they are all at the same energy level.

Statistically this means that they are all equally probable of being filled, and in quantum mechanics it is represented mathematically by the Hamiltonian for the system having more than one linearly independent eigenstate with the same eigenvalue.

Conversely, an energy level is said to be degenerate if it contains two or more different states.

The number of different states at a particular energy level is called the level's degeneracy, and this phenomenon is generally known as a quantum degeneracy.