Degenerate energy level Totally Explained

Everything about Degenerate Energy Level totally explained

ť This article refers to physical states having the same energy. For other uses of the word degeneracy, see degeneracy (disambiguation).

In physics two or more different physical states are said to be degenerate if they're all at the same energy level. Physical states differ if and only if they're linearly independent. 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.
In quantum theory this usually pertains to electronic configurations and the electron's energy levels, where different possible occupation states for particles may be related by symmetry. The usage comes from the fact that degenerate eigenstates correspond to identical eigenvalues of the Hamiltonian. Since eigenvalues correspond to roots of the characteristic equation, degeneracy here has the same meaning as the common mathematical usage of the word.
If the symmetry is broken by a, such as applying an external electric field, this can change the energies of the states, causing energy level splitting.

In electromagnetics, degeneracy refers to modes of propagation which exist at the same frequency and longitudinal propagation constant. As an example, for a rectangular waveguide, the TE_mn mode is degenerate to the TM_mn mode if m and n are the same for both of them.

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