Kvantnumbrist

Kvantnumbrist is a term used in some Swedish-language discussions to describe a situation in quantum theory where the set of quantum numbers available to label states is insufficient to uniquely identify them. Put differently, there is a quantum-number deficit in the sense that the chosen labels do not fully distinguish the eigenstates of a system.

In quantum mechanics, eigenstates of a Hamiltonian are typically labeled by a collection of commuting observables, and each observable provides a quantum number. If the Hamiltonian exhibits degeneracies that cannot be resolved by this chosen set of observables, multiple distinct states share the same quantum-number labels. This incomplete labeling can complicate the construction of a complete basis and the interpretation of the spectrum.

Kvantnumbrist arises in contexts where symmetries are incomplete or partially hidden. It can occur when a system has additional, non-obvious or dynamical symmetries that are not captured by the conventional set of quantum numbers, or when symmetry-breaking interactions mix states in ways that ordinary labels no longer distinguish. In practice, the deficit motivates extending the labeling scheme by incorporating extra observables, employing group-theoretical methods, or using Casimir invariants and symmetry-adapted bases to reveal a more complete set of quantum numbers.

Applications of the concept appear across areas such as atomic, nuclear, and condensed-matter physics, particularly in modeling systems with complex interactions or partially broken symmetries. Kvantnumbrist highlights the importance of choosing a complete and appropriate labeling scheme for accurate state classification and spectral analysis.