What is a non-degenerate state
Degeneracy (quantum mechanics)
Of degeneration In quantum mechanics, one speaks when two or more states of a quantum mechanical system exist with the same energy.
The Degree of degeneration n is the number of linearly independent solutions to the same energy eigenvalue. To have n States of the same energy, one speaks of n-fold degeneration.
The degenerate states differ in the values of another observable (observable quantity, e.g. the orbital angular momentum or the total angular momentum), one then says that the states are in this observable degenerate.
A degeneracy is generally the result of a symmetry of the physical system. So rotational symmetry leads to a degeneracy in any component of the angular momentum with a fixed amount of the same.
For example, in the non-relativistic description of the hydrogen atom, all states with the same principal quantum number are degenerate. This degeneracy can be traced back to the symmetry of the Kepler problem.
The consideration of relativistic corrections (the so-called fine structure) partially eliminates this degeneracy, corrections due to the interaction with the nucleus (hyperfine structure) and due to quantum electrodynamics (lambshift) reduce the degeneracy further down to the degeneracy in the components of the total angular momentum due to the rotational symmetry .
Category: quantum physics
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