Short-range oscillators in a power-series picture

DOI10.1088/0305-4470/33/8/309zbMATH Open1043.81531arXivquant-ph/9909068OpenAlexW3098291827MaRDI QIDQ4495970

Publication date: 13 August 2000

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: A class of short-range potentials on the line is considered as an asymptotically vanishing phenomenological alternative to the popular confining polynomials. We propose a method which parallels the analytic Hill-Taylor description of anharmonic oscillators and represents all our Jost solutions non-numerically, in terms of certain infinite hypergeometric-like series. In this way the well known solvable Rosen-Morse and scarf models are generalized.

Full work available at URL: https://arxiv.org/abs/quant-ph/9909068

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05)

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