The quantum-mechanical system whose potential is the cusp catastrophe is studied. The qualitative features of this system, including the eigenvalue spectrum, density of states, wave-function localization and delocalization, probability distribution, operator expectation values, and matrix elements, are studied as functions of the cusp control parameter values. Canonical features preceding and accompanying the transition from the single-mode to the double-mode regime have been determined. The relationships between the qualitative properties of the quantum cusp and the canonical properties of the cusp catastrophes are exhibited.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)