In
quantum mechanics, an
energy level is said to be degenerate if it corresponds to two or more different measurable states of a quantum system. Conversely, two or more different states of a quantum mechanical system are said to be
degenerate if they give the same value of energy upon measurement. The number of different states corresponding to a particular energy level is known as the degree of degeneracy of the level. It is represented mathematically by the
Hamiltonian for the system having more than one
linearly independent eigenstate with the same
eigenvalue. In
classical mechanics, this can be understood in terms of different possible trajectories corresponding to the same energy.