Degeneracy

Definition

Degeneracy refers to a situation in quantum mechanics where two or more different quantum states share the same energy level. This concept is crucial because it indicates that a system can have multiple configurations with identical energy, leading to interesting physical properties and symmetries. Understanding degeneracy helps explain phenomena such as the stability of certain states and the behavior of particles in various potentials.

5 Must Know Facts For Your Next Test

1. Degeneracy arises in systems with symmetries, allowing for multiple states to correspond to the same energy level.
2. In quantum mechanics, degeneracy can be lifted through interactions or external fields, causing different energy levels to separate.
3. Degenerate states can be classified into different categories based on their symmetry properties, such as orbital and spin degeneracies.
4. The presence of degeneracy can lead to phenomena like the stability of certain molecular structures and the behavior of electrons in metals.
5. In systems like the hydrogen atom, the degeneracy is observed in the electronic states corresponding to different angular momentum quantum numbers.

Review Questions

• How does degeneracy relate to the stability of quantum states in a physical system?
  • Degeneracy contributes to the stability of quantum states because when multiple configurations exist at the same energy level, small perturbations or changes may not significantly affect the overall energy. This allows the system to maintain stability across various conditions. For example, in a degenerate system, if one state is perturbed slightly, the others can adjust, maintaining a similar energy configuration and thus preserving stability.
• What role does symmetry play in creating degenerate states, and how can this symmetry be broken?
  • Symmetry plays a fundamental role in creating degenerate states by allowing different quantum states to exist at the same energy level due to their invariant properties under certain transformations. For instance, a spherical potential allows multiple angular momentum states to have the same energy. However, if an external field or interaction is introduced that disrupts this symmetry—such as applying an electric field—degeneracy can be lifted, leading to distinct energy levels for previously degenerate states.
• Evaluate the implications of degeneracy on electronic structure and behavior in materials like metals.
  • The implications of degeneracy on electronic structure in materials like metals are significant because it affects their conductive properties. In metals, electrons occupy degenerate states near the Fermi level, allowing for increased mobility and conductivity. When these degenerate states are influenced by external factors such as temperature or magnetic fields, it can lead to changes in electrical resistance and other material properties. Understanding degeneracy helps explain phenomena such as superconductivity and magnetoresistance in these materials.

Related terms

Energy Levels: Discrete values of energy that an electron can have in an atom, determined by the quantum state of the electron.

Symmetry:

A property of a physical system that remains invariant under certain transformations, often associated with conservation laws.

Quantum States: The complete description of a quantum system, including its properties such as position, momentum, and spin, represented mathematically by wavefunctions.