Summary
In a previous paper we showed that an extended Schrödinger equation (ESE) can lead to critical phenomena. The ESE was defined as an integro-differential Schrödinger equation obtained from the traditional differential Schrödinger equation by extending the local potential to a non-local potential. Here we pursue further this procedure by constructing a class of such ESE which is able to generate the (quantum) squeezing phenomenon. As an example, we discuss a model by Glauber for particle trapping by oscillating fields, in the present perspective.
Similar content being viewed by others
References
Baseia B.,J. Math. Phys.,30 (1989) 81
Wataghin G.,Z. Phys.,88 (1934) 92;Nuovo Cimento,9 (1958) 519.
Yamaguchi Y.,Phys. Rev.,95 (1954) 1628;Tabakin F.,Phys. Rev.,174 (1968) 1208.
Austern N.,Phys. Rev.,131 (1965) 752;Perey F. G. andBuck B.,Nucl. Phys.,32 (1962) 353;Perey F. G. andSaxon D. S.,Phys. Lett.,10 (1964) 107.
Gottfried K,Quantum Mechanics (Benjamin, New York, N.Y.) 1956;Massey H. S.,Theory of Atomic Collision (Clarendon, Oxford) 1965, p. 181;Bohr A. andMottelson B.,Nuclear Structure (Benjamin, New York, N.Y) 1969, p. 217;McCarthy I. E.,Introduction to Nuclear Theory (Wiley, New York, N.Y) 1968, p. 77.
Cohen-Tannoudji C., Dupont-Roc J. andGrynberg G. Photons and Atoms (Wiley and Sons, New York, N.Y.) 1989, pp. 14, 15.
Huen H. P.,Phys. Rev. A,13 (1976) 2226;Walls D. F.,Nature,306 (1983) 141;Loudon R. andKnight P. L.,J. Mod. Opt.,33 (1981) 709;Cohen-Tannoudji C., Du Pont-Roc J. andGrinberg G.,Photons and Atoms (Wiley and Sons, New York, N.Y.) 1989, p. 241.
Glauber R.,Quantum Theory of Particle Trapping by Oscillating Fields, Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138, HUTP-91/B001; see alsoThe Quantum Mechanics of Trapped Wave Packets, Proceedings of the International Summer School of Physics Enrico Fermi, Varenna, Italy, Course CXVIII edited byE. Arimondo, W. Phillips andF. Strumia (North-Holland) 1992, p. 643.
Baseia B., Bagnato V. S. andVyas R.,Quantum Opt.,5 (1993) 155;6 (1994) 73.
Author information
Authors and Affiliations
Additional information
The authors of this paper have agreed to not receive the proofs for correction.
Rights and permissions
About this article
Cite this article
Baseia, B., Dias, H., Dantas, C.M.A. et al. Extended Schrödinger equation leading to squeezing phenomena. Nuov Cim B 111, 287–292 (1996). https://doi.org/10.1007/BF02724652
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02724652