Propagators of isochronous an-harmonic oscillators and Mehler formula for the exceptional Hermite polynomials

摘要

It is shown that fundamental solutions K-sigma (x, y; t) = < x vertical bar e(-iH sigma t) vertical bar y > of the non-stationary Schrodinger equation (Green functions, or propagators) for the rational extensions of the Harmonic oscillator H-sigma = H-osc + Delta V-sigma are expressed in terms of elementary functions only. An algorithm to calculate explicitly K-sigma for an arbitrary increasing sequence of positive integers sigma is given, and compact expressions for K-{1.2} and K-{2.3} are presented. A generalization of Mehler's formula to the case of exceptional Hermite polynomials is given. (C) 2015 Elsevier Inc. All rights reserved.