Noncommuting limits of oscillator wave functions

J. Daboul, G. S. Pogosyan, K. B. Wolf

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Quantum harmonic oscillators with spring constants k > 0 plus constant forces f exhibit rescaled and displaced Hermite-Gaussian wave functions, and discrete, lower bound spectra. We examine their limits when (k, f) → (0, 0) along two different paths. When f → 0 and then k → 0, the contraction is standard: the system becomes free with a double continuous, positive spectrum, and the wave functions limit to plane waves of definite parity. On the other hand, when k → 0 first, the contraction path passes through the free-fall system, with a continuous, nondegenerate, unbounded spectrum and displaced Airy wave functions, while parity is lost. The subsequent f → 0 limit of the nonstandard path shows the dc hysteresis phenomenon of noncommuting contractions: the lost parity reappears as an infinitely oscillating superposition of the two limiting solutions that are related by the symmetry.

Original languageEnglish
Pages (from-to)513-519
Number of pages7
JournalPhysics of Atomic Nuclei
Volume70
Issue number3
DOIs
StatePublished - 1 Mar 2007
Externally publishedYes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Nuclear and High Energy Physics

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