New SUSYQM coherent states for Poschl-Teller potentials: a detailed mathematical analysis

0385113 - ÚJF 2013 RIV FR eng J - Journal Article
Bergeron, H. - Siegl, Petr - Youssef, A.
New SUSYQM coherent states for Poschl-Teller potentials: a detailed mathematical analysis.
Journal of Physics A-Mathematical and Theoretical. Roč. 45, č. 24 (2012), 244028/1-244028/14. ISSN 1751-8113. E-ISSN 1751-8121
R&D Projects: GA MŠMT LC06002; GA ČR GAP203/11/0701
Institutional support: RVO:61389005
Keywords : supersymmetry * Poschi-Teller potential
Subject RIV: BE - Theoretical Physics
Impact factor: 1.766, year: 2012

In a recent short note (Bergeron et al 2010 Europhys. Lett. 92 60003), we have presented the good properties of a new family of semi-classical states for Poschl-Teller potentials. These states are built from a supersymmetric quantum mechanics (SUSYQM) approach and the parameters of these 'coherent' states are points in the classical phase space. In this paper, we develop all the mathematical aspects that have been left out of the previous paper (proof of the resolution of unity, detailed calculations of the quantized version of classical observables and mathematical study of the resulting operators: problems of domains, self-adjointness or self-adjoint extensions). Some additional questions such as asymptotic behavior are also studied. Moreover, the framework is extended to a larger class of Poschl-Teller potentials.
Permanent Link: http://hdl.handle.net/11104/0216923