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arXiv · 1502.01778

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

Andrey M. Pupasov-Maksimov
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Abstract

It is shown that fundamental solutions $K^σ(x,y;t)=\langle x|e^{-i H^σt}|y\rangle$ of the non-stationary Schrödinger equation (Green functions, or propagators) for the rational extensions of the Harmonic oscillator $H^σ=H_{\rm osc}+ΔV^σ$ are expressed in terms of elementary functions only. An algorithm to calculate explicitly $K_σ$ for an arbitrary $σ\in \mathbb{N}$ is given, compact expressions for $K^{\{1,2\}}$ and $K^{\{2,3\}}$ are presented. A generalization of the Mehler's formula to the case of exceptional Hermite polynomials is given.

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Andrey M. Pupasov-Maksimov. 2015-02-06. Propagators of isochronous an-harmonic oscillators and Mehler formula for the x-Hermite polynomials. https://arxiv.org/abs/1502.01778

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