Isospectrality of conventional and new extended

potentials, second-order supersymmetry and role

of PT symmetry

B BAGCHI^1,*, C QUESNE² and R ROYCHOUDHURY³

¹Department of Applied Mathematics, University of Calcutta,

92 Acharya Prafulla Chandra Road, Kolkata 700 009, India

²Physique Nucl\'eaire Th\'eorique et Physique Math\'ematique,

Universit\'e Libre de Bruxelles, Campus de la Plaine CP229,

Boulevard~du Triomphe, B-1050 Brussels, Belgium

³Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700 035, India

^*Corresponding author

E-mail: bbagchi123@rediffmail.com; cquesne@ulb.ac.be; rajdaju@rediffmail.com

Abstract. We develop a systematic approach to construct novel

completely solvable rational potentials. Second-order supersymmetric

quantum mechanics dictates the latter to be isospectral to some

well-studied quantum systems. PT symmetry may facilitate

reconciling our approach to the requirement that the rationally

extended potentials be singularity free. Some examples are shown.

Keywords. Exact solvability; supersymmetry; PT symmetry;

rational potentials.

PACS Nos 03.65.Fd; 03.65.Ge