Quantum degeneracy refers to a situation in quantum mechanics where multiple quantum states have the same energy. In other words, it occurs when different quantum states correspond to the same energy level or eigenvalue.
Degeneracy arises due to the mathematical properties of the quantum mechanical equations that describe a physical system. In a non-degenerate system, each energy level corresponds to a unique quantum state. However, in degenerate systems, multiple quantum states can have the same energy.
This concept is particularly relevant in quantum systems with symmetries. Symmetries in a physical system can give rise to degeneracy by imposing constraints on the possible quantum states and their corresponding energies. For example, in a spherically symmetric potential, such as the hydrogen atom, the energy levels are degenerate in terms of the total angular momentum quantum number.
Degeneracy has important implications in various areas of physics, including atomic and molecular physics, solid-state physics, and quantum field theory. Some notable phenomena associated with degeneracy include the Zeeman effect, where degeneracy is lifted in the presence of a magnetic field, and the degenerate electron gas in condensed matter physics.
Understanding and characterizing degeneracy in quantum systems is crucial for accurately predicting and interpreting experimental results. Degenerate states can have distinct physical properties and behaviors, and their analysis often requires techniques from symmetry theory and group representations.
Overall, quantum degeneracy refers to the situation where multiple quantum states share the same energy level, and it plays a significant role in understanding the behavior of quantum systems and their symmetries.