What is Degeneracy in Quantum Mechanics? Explained (with Examples)

What is Degeneracy in Quantum Mechanics? I explain it using the example of Particle in a 3D Box.

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QM LEC 35
In quantum mechanics, degeneracy refers to the situation where two or more distinct quantum states share the same energy level. These states are said to be degenerate. Degeneracy typically arises due to symmetries in the system, where the system’s Hamiltonian (which describes its energy) has certain symmetries that lead to multiple states having the same energy.

Degeneracy plays a crucial role in various quantum systems, influencing how systems respond to perturbations and how they behave in fields such as statistical mechanics and quantum computing.

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