Perturbed Poeschl-Teller oscillators

TL;DR

This paper develops a Lanczos-inspired perturbation theory to analytically compute wave functions and energies of a perturbed Poeschl-Teller oscillator using a non-orthogonal basis, with results generated via MAPLE.

Contribution

It introduces a novel perturbation approach with closed-form corrections for the Poeschl-Teller oscillator using a non-orthogonal basis.

Findings

Closed-form perturbation corrections derived

Wave functions and energies computed analytically

Results generated with MAPLE software

Abstract

Wave functions and energies are constructed in a short-range Poeschl-Teller well (= negative quadratic secans hyperbolicus) with a quartic perturbation. Within the framework of an innovated, Lanczos-inspired perturbation theory we show that our choice of non-orthogonal basis makes all the corrections given by closed formulae. The first few items are then generated using MAPLE.