TY - JOUR

T1 - Noncommuting limits of oscillator wave functions

AU - Daboul, J.

AU - Pogosyan, G. S.

AU - Wolf, K. B.

N1 - Funding Information:
We acknowledge support from the SEP– CONACYT project 44845, Optica, Matemática, and DGAPA–UNAM project no. IN102603; and the help of Guillermo Krötzsch and Luis Edgar Vicent with the figures. The work of G.S.P. also has been partially supported by proyecto de PROMEP/103.5/05/1705/.

PY - 2007/3/1

Y1 - 2007/3/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34147142875&partnerID=8YFLogxK

U2 - 10.1134/S1063778807030106

DO - 10.1134/S1063778807030106

M3 - Article

AN - SCOPUS:34147142875

SN - 1063-7788

VL - 70

SP - 513

EP - 519

JO - Physics of Atomic Nuclei

JF - Physics of Atomic Nuclei

IS - 3

ER -