Degeneracy in quantum mechanics refers to the situation where multiple quantum states have the same energy level. This means that the different quantum states are indistinguishable from one another and cannot be uniquely identified by their energy levels.
Degeneracy can occur in quantum systems due to symmetries in the system, such as rotational or reflection symmetries. These symmetries result in different quantum states having the same energy level, leading to degeneracy.
Degeneracy plays an important role in quantum mechanics as it allows for multiple quantum states to have the same energy level, providing a greater variety of possible states for a system. It also allows for the existence of degenerate ground states, which can have important implications in certain physical phenomena.
Degeneracy can be broken in quantum systems by introducing perturbations or external fields that break the symmetries present in the system. This results in the energy levels of the different quantum states becoming different and the degeneracy being lifted.
Degeneracy in quantum mechanics is related to the uncertainty principle in that it reflects the limitations of our ability to measure and predict the exact state of a quantum system. The uncertainty principle states that the more precisely we know the energy of a particle, the less precisely we can know its position, and vice versa. Degeneracy adds another layer of uncertainty as we cannot determine which specific quantum state a particle is in if there are multiple degenerate states with the same energy level.