Generalized coherent states of exceptional Scarf-I potential: Their spatio-temporal and statistical properties

Abstract

We construct generalized coherent states for the rationally extended Scarf-I potential. Statistical and geometrical properties of these states are investigated. Special emphasis is given to the study of spatio-temporal properties of the coherent states via the quantum carpet structure and the auto-correlation function. Through this study, we aim to find the signature of the `"rationalisation" of the conventional potentials and the classical orthogonal polynomials.

33 figures. Accepted for publication in Reviews in Mathematical Physics

References in corpus (4)

• Infinitely many shape invariant potentials and new orthogonal polynomials
• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Exceptional orthogonal polynomials and the Darboux transformation
• Coherent states for ladder operators of general order related to exceptional orthogonal polynomials