New exactly solvable isospectral partners for symmetric potentials

2003/12/18 by Anjana Sinha, Pinaki Roy
Chemistry · Mathematics · Physics and Astronomy · #Chemistry #Darboux integral #Geometry #Hamiltonian (control theory) #Hermitian matrix #Isospectral #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Simple (philosophy) #Symmetry (geometry) #Transformation (genetics) #quant-ph

paper · pdf · doi:10.1088/0305-4470/37/6/039

11 pages, 2 figures, To be published in Journal of Physics A (2004)

arxiv created 2003/12/18 · openalex publication_date 2004/01/28 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We examine, in detail, the possibility of applying the Darboux transformation to non-Hermitian Hamiltonians. In particular we propose a simple method of constructing exactly solvable symmetric potentials by applying Darboux transformation to higher states of an exactly solvable symmetric potential. It is shown that the resulting Hamiltonian and the original one are pseudo supersymmetric partners. We also discuss application of the Darboux transformation to Hamiltonians with spontaneously broken symmetry.

Citations

• Conditions for complex spectra in a class of PT symmetric potentials
• Non-Hermitian supersymmetry and singular, 𝒫𝒯-symmetrized oscillators
• Supersymmetry and Quantum Mechanics
• Second order SUSY transformations with ‘complex energies’
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the coordinate: real spectrum of complex potentials