First-Order Intertwining Operators with Position Dependent Mass and η-Weak-Pseudo-Hermiticity Generators

2006/07/31 by Omar Mustafa, S. Habib Mazharimousavi · 2 citations
Chemistry · Mathematics · Physics and Astronomy · #Hermitian matrix #Isospectral #Mathematical physics #Mathematics #Order (exchange) #Physics #Position (finance) #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Synthesis and Properties of Aromatic Compounds #quant-ph

paper · pdf · doi:10.1007/s10773-007-9470-7

published as Int. J. Theor. Phys. 47, 446 (2008) · 11 pages, no figures, Revised/Expanded, more references added. To appear in the Int.J. Theor. Phys

arxiv created 2007/04/16 · openalex publication_date 2007/06/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of η-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target η-weak-pseudo-Hermitian PDM -- Hamiltonians' map is suggested. Some η-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-levels crossing and flown-away states phenomena are reported for the resulting Scarf II spectrum. Some of the corresponding η-weak-pseudo-Hermitian Scarf II- and periodic-type-isospectral models (PT -symmetric and non-PT -symmetric) are given as products of the reference-target map.

Citations

• Pseudo-hermitian interaction between an oscillator and a spin half particle in the external magnetic field
• Deformed algebras, position-dependent effective masses and curved spaces: an exactly solvable Coulomb problem
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the coordinate: real spectrum of complex potentials
• First-order intertwining operators and position-dependent mass Schrödinger equations in d dimensions

Cited by

• Analytical Solutions to the Klein–Gordon Equation with Position-Dependent Mass for q -Parameter Pöschl–Teller Potential
• Position-dependent mass, finite-gap systems, and supersymmetry