Articles by others on the same topic
An energy level is degenerate when its eigenspace has dimension greater than one: several linearly independent energy eigenstates share the same energy eigenvalue. Any quantum superposition within that eigenspace is also an energy eigenstate with the same energy.
For a particle in a ring without applied flux, clockwise and anticlockwise momentum eigenstates have equal kinetic energy, except for the single zero-momentum state. A field or other perturbation may split such a pair if it distinguishes the two states. Degenerate perturbation theory identifies the combinations selected by a weak perturbation. The energy-level degeneracy counts independent states, rather than the number of different basis descriptions one can write for them.