In quantum mechanics, an energy level is 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 … See more

The possible states of a quantum mechanical system may be treated mathematically as abstract vectors in a separable, complex Hilbert space, while the observables may be represented by linear Hermitian operators acting upon them. By selecting … See more

If two operators $${\displaystyle {\hat {A}}}$$ and $${\displaystyle {\hat {B}}}$$ commute, i.e., $${\displaystyle [{\hat {A}},{\hat {B}}]=0}$$, then for every eigenvector See more

Degeneracies in a quantum system can be systematic or accidental in nature.
Systematic or essential degeneracy
This is also called a geometrical or normal degeneracy and … See more

This section intends to illustrate the existence of degenerate energy levels in quantum systems studied in different dimensions. The study of one and two-dimensional systems … See more

The physical origin of degeneracy in a quantum-mechanical system is often the presence of some symmetry in the system. Studying the symmetry of a quantum system can, in some cases, enable us to find the energy levels and degeneracies without … See more

The hydrogen atom
In atomic physics, the bound states of an electron in a hydrogen atom show us useful examples of degeneracy. In this case, the Hamiltonian commutes with the total orbital angular momentum See more