On the Liouville transformation and exactly-solvable Schrodinger equations

1997/06/15 by Robert Milson, Milson, Robert
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Quantum and Classical Electrodynamics #Spectral Theory in Mathematical Physics #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9706007

16 pages, 6 figures

openalex publication_date 1997/06/15 · arxiv created 1997/10/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present article discusses the connection between exactly-solvable Schrodinger equations and the Liouville transformation. This transformation yields a large class of exactly-solvable potentials, including the exactly-solvable potentials introduced by Natanzon. As well, this class is shown to contain two new families of exactly solvable potentials.

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