PT-Symmetric Solutions of Schrödinger Equation with Position-Dependent Mass via Point Canonical Transformation

2006/04/06 by Cevdet Tezcan, C. Tezcan, R. Sever +1 · 10 citations
Mathematics · Physics and Astronomy · #Canonical transformation #Eigenvalues and eigenvectors #Harmonic oscillator #Mathematical analysis #Mathematical physics #Mathematics #Physics #Position (finance) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Schrödinger equation #Transformation (genetics) #Wave function #quant-ph

paper · pdf · doi:10.1007/s10773-007-9589-6

published in International Journal of Theoretical Physics 47(5), 1471-1478 (Springer Science+Business Media) · 12 pages

arxiv created 2006/04/06 · openalex publication_date 2007/10/22 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05

Abstract

Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical transformation is introduced by using a free parameter. Two different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.

Citations

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• A PT-invariant potential with complex QES eigenvalues
• SUPERSYMMETRIC APPROACH TO EXACTLY SOLVABLE SYSTEMS WITH POSITION-DEPENDENT EFFECTIVE MASSES
• Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe
• EXACT SOLUTIONS OF EFFECTIVE-MASS SCHRÖDINGER EQUATIONS