SUSY partners for spin-1/2 systems in nonrelativistic limits

• Autorzy: Daniel Sabi Takou , Gabriel Y.H. Avossevou , Basile B. Kounouhewa
• Języki publikacji: EN

Abstrakty

EN

In this paper, we use some well-known techniques of Supersymmetric QuantumMechanics (SUSYQM) namely the factorization method and shape invariance, to generate new analytically solvable potentials from some interacting fermionic models in nonrelativistic limits. These systems are described by the ordinary and the harmonically trapped Schrödinger-Pauli particle models and the Dirac-Coulomb Hamiltonian, this latter being set in its nonrelativistic limits. The spectrum for each of these models is obtained in a simple and transparent way. We then generate new solvable potentials that describe interactions between electromagnetic field and matter, paying due attention to the subtleties inherent in the application of SUSY to higher dimensional problems. SUSY breaking problems related to the partner singularities are dicussed along with the paper.

Słowa kluczowe

EN

supersymmetry (SUSY); Pauli-Schrödingerequation; Dirac-Coulomb system; SUSY partners; singularity

• Czasopismo: Open Physics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2014-08-03

zaakceptowano

2014-12-01

online

2015-02-04

Twórcy

autor

Daniel Sabi Takou

• Unité de Recherche en Physique Théorique
  (URPT), Institut de Mathématiques et de Sciences Physiques (IMSP),
  01 B.P. 613 Porto-Novo, Rep. du Bénin

autor

Gabriel Y.H. Avossevou

• Unité de Recherche en Physique Théorique
  (URPT), Institut de Mathématiques et de Sciences Physiques (IMSP),
  01 B.P. 613 Porto-Novo, Rep. du Bénin
• Département de Physique, Faculté des
  Sciences et Techniques (FAST), Université d’Abomey-Calavi (UAC),
  Rep. du Bénin

autor

Basile B. Kounouhewa

• Département de Physique, Faculté des
  Sciences et Techniques (FAST), Université d’Abomey-Calavi (UAC),
  Rep. du Bénin

Bibliografia

• [1] R. Dutt, A. Khare, U. Sukhatme, Am. J. Phys. 56, 163 (1988)
• [2] F. Cooper, A. Khare, U. Sukhatme, Phys. Rep. 251, 267 (1995)
• [3] F. Cooper, A. Khare, U. Sukhatme, Supersymmetry in QuantumMechanics (World Scientific, Singapore, 2001)
• [4] D.B. Iyela, J. Govaerts, M.N. Hounkonnou, arXiv: 1209.0182v1[WoS]
• [math-ph] (2012)]
• [5] J. Govaerts, Quantum Physics and Factorization Methods:An Introductory Overview; lectures delivered at the 2012African Mathematical Union (AMU) School held at the InternationalChair in Mathematical Physics and Applications (ICMPA),Cotonou, Benin, 29 October – 9 November 2012 (unpublished)
• [6] A.G. Nikitin, J. Math. Phys. 53, 122103, (2012)[Crossref]
• [7] A.G. Nikitin, J. Phys. A: Math. Theor. 45, 485204 (2012)[Crossref]
• [8] L.E. Gendenshtein, Pisma Zh. Eksp. Teor. Fiz. 38, 299 (1983) (Englishtranslation in JETP Lett. 38, 356 (1983))
• [9] E. Witten, Nucl. Phys. B 202, 253 (1982)
• [10] L. Infeld, T.E. Hull, Rev. Mod. Phys. 23, 21 (1951)[Crossref]
• [11] E. Schrödinger, Proc. R. Irish Acad. A 46, 9 (1941)
• [12] B.K. Bagchi, Supersymmetry in quantum and classical mechanics(CHAPMAN and HALL/CRC, Monographs and Surveys in Pureand Applied Mathematic, Boca Raton, Florida, 2001)
• [13] M. Abramowitz, I. Stegun, Handbook ofMathematical Functions(Dover, New York, 1965)
• [14] C. Itzykson, J-B. Zuber, Quantum Field Theory (Mc Graw-Hill,New York, 1985)
• [15] B. Thaller, The Dirac Equation (Springer-Verlag, Berlin Heidelberg,1992)
• [16] A. Nikiforov, V. Ouvarov, Fonctions Spéciales de la PhysiqueMathématique (Traduction française Editions MIR, Moscou,1983)
• [17] D.T. Barclay, R. Dutt, A. Gangopadhyaya, A. Khare, A. Pagnamenta,U. Sukhatme, Phys. Rev. A 48, 2786 (1993)
• [18] D.T. Barclay, A. Khare, U. Sukhatme, UICHEP-TH/93-13 (1993)
• [19] M. Robnik, L. Salasnich, J. Phys. A: Math. Gen. 30, 1711 (1997)[Crossref]
• [20] A. Inomata, G. Junker, In H.A. Cerdeira et al. (Eds.), Lecturesin Path Integration: Trieste, Italy (World Scientific, Singapore,1993)
• [21] J. López-Bonilla1, J. Morales, G. Ovando, Apeiron, 9, 20 (2002)
• [22] J.H. Caltenco, J. López-Bonilla, M.A. Acevedo, Acta Acad. Paedagog.Agriensis Sect. Mat. 31, 121 (2004)
• [23] B.F. Samsonov, arxiv:quant-ph/9904009v1
• [24] H.R. Lewis, W.B. Riesenfeld, J. Math. Phys. 10, 1458 (1969)[Crossref]
• [25] B. Mielnik, in (QTS8), J. Phys: Conference Series 512, 012035(2014)
• [26] A.D. Alhaidari, Mod. Phys. Lett. A 21, 581 (2006)
• [27] J.-P. Gazeau, Coherent States in Quantum Physics (Wiley-VCH,Berlin, 2009)
• [28] J.R. Klauder, Enhanced Quantum Procedures that Resolve Dif-ficult Problems, Lecture Notes for the Advanced Scholar Seminar,Interaction of Mathematics and Physics: New Perspectives(Moscow, Russia 2012)
• [29] J.R. Klauder, J. Phys. A 45, 285304 (2012)
• [30] J.R. Klauder, arXiv : 1206.4017, 2012 [hep-th]
• [31] M. Molski, J. Phys A: Math. Theor. 42, 165301 (2009)[Crossref]
• [32] J.-P. Antoine, J.-P.Gazeau, P. Monceau, J.R. Klauder, K.A. Penson,J. of Math. Phys. 42, 2349, (2001)[Crossref]

Identyfikatory

DOI

10.1515/phys-2015-0021