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

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 PDMHamiltonians' 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.

Position-dependent mass, finite-gap systems, and supersymmetry

“…Another interesting generalization of the approach presented here would be its application to the study of the PT symmetric quantum systems. Some investigations of the systems with PDM in the context of PT symmetry were realized in [21,22,23].…”

“…Quantum mechanical systems with PDM were employed recently in the context of integrable models [12]. They turn out to be interesting from the point of view of supersymmetric quantum mechanics [13,14,15,16,17], coherent states [18,19,20], and PT-symmetry [21,22,23]. Besides the onedimensional quantum systems with PDM, their multi-dimensional generalizations are considered in the literature [24,25,26,27,28,29], particularly, in the context of superintegrable systems [30,31].…”

The generalized Klein–Gordon oscillator in the background of cosmic string space-time with a linear potential in the Kaluza–Klein theory

“…The relativistic quantum dynamics of a scalar particle in 4D curved space-time with the cosmic string was investigated in [10]. The relativistic quantum dynamics of scalar and spin- 1 2 particles subject to various kind of potentials have been investigated in several areas of physics (e. g., [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]). Linear confinement of quantum particle by introducing a linear scalar potential into the relativistic system by modifying the mass term has great importance for models of confinement of quarks [26].…”

Analytical Solution of the Schrödinger Equation with Spatially Varying Effective Mass for Generalised Hylleraas Potential

“…Several authors have studied the effects of the position-dependent mass on the solutions of the Schrödinger equation. A positiondependent effective mass, ( ) = 1 ⋅ ( ), associated with a quantum mechanical particle constitutes a useful model for the study of various potentials such as Morse potential [12][13][14][15][16][17][18], hard-core potential [18], Scarf potential [19][20][21], Pöschl-Teller potential [22,23], spherically ring-shaped potential [24], Hulthén potential [25], Kratzer potential [26], and Coulomb-like potential [27,28]. Different techniques have been developed to obtain its exact solutions, such as factorization methods [29], Nikiforov-Uvarov (NU) methods [30], and supersymmetric quantum mechanics [31].…”