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 -