Degeneracy:

Degeneracy is when 1 energy level corresponds to 2 or more states of motion.  It occurs when the symmetry of a molecule is such that certain fundamental frequencies are equal and is a common feature in IR spectroscopy. It states that 2 or more stationary states of the same quantum-mechanical system can posses the same energy even if their wave functions are not the same. In this case common energy level of the stationary states is degeneracy. Degeneracy is a state of matter attained when atomic particles are packed together as tightly as possible physically, at densities of several thousand tones per cubic meter. The particles which are very close together are forbidden by Pauli Exclusion Principle to have the same energy, and, as a result of which, the particles repel each other. This creates degeneracy pressure. The energy state having more than 1 wave function for the same value of energy is known as degenerate state and the phenomenon is known as degeneracy.

Degenerate matter is a highly compressed phase of matter where all or some of the electron orbits have been distorted from pressure. It can be characterized by great density and consisting of atoms stripped of electrons. The degenerate energy levels is a different form of the physical system which have same energy. It relates to 2 or more quantum states which share the same quantum numbers. It pressure is the pressure exerted by a degenerate electron or neutron gas. Degenerate is having quantum states with the same energy.  The electron degeneracy is the state of degeneracy attained when the density of matter is so high that the electrons can't be packed any closer. Electron degeneracy supports white dwarf stars against the further collapse. The only other type of degeneracy in huge objects is the neutron degeneracy found in neutron stars. Degenerate orbitals are orbitals which are having the same energy. This degeneracy can at times be lifted by external electric or magnetic fields.