Quantum cusp

R. Gilmore, S. Kais, R. D. Levine

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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.

Original languageEnglish
Pages (from-to)2442-2452
Number of pages11
JournalPhysical Review A
Issue number3
Publication statusPublished - 1 Dec 1986
Externally publishedYes


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Physics and Astronomy(all)

Cite this

Gilmore, R., Kais, S., & Levine, R. D. (1986). Quantum cusp. Physical Review A, 34(3), 2442-2452. https://doi.org/10.1103/PhysRevA.34.2442