Exact solvability of potentials with spatially dependent effective masses

DOI10.1016/S0375-9601(00)00533-8zbMath1115.81396arXivquant-ph/0306065WikidataQ128089932 ScholiaQ128089932MaRDI QIDQ998036

J. Martínez

Publication date: 10 August 2007

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0306065

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Exactly and quasi-solvable systems arising in quantum theory (81U15)

Related Items

Properties of quasi-oscillator in position-dependent mass formalism ⋮ Position-dependent-mass: cylindrical coordinates, separability, exact solvability and \mathcal {PT} -symmetry ⋮ PDM Klein-Gordon oscillators in cosmic string spacetime in magnetic and Aharonov-Bohm flux fields within the Kaluza-Klein theory ⋮ Discrete fractional solutions to the effective mass Schrödinger equation by mean of nabla operator ⋮ Position-dependent mass Dirac equation and local Fermi velocity ⋮ Quantum information entropies for a soliton at hyperbolic well ⋮ The quantum harmonic oscillator on the sphere and the hyperbolic plane ⋮ Solution of the Dirac equation with position-dependent mass in the Coulomb field ⋮ Series solutions of the Schrödinger equation with position-dependent mass for the Morse potential ⋮ Mapping between charge-monopole and position-dependent mass systems ⋮ A squeeze-like operator approach to position-dependent mass in quantum mechanics ⋮ A quantum quasi-harmonic nonlinear oscillator with an isotonic term ⋮ Harmonic oscillators from displacement operators and thermodynamics ⋮ Approximate solution of the effective mass Klein-Gordon equation for the Hulthen potential with any angular momentum ⋮ SUPERSYMMETRIC APPROACH TO EXACTLY SOLVABLE SYSTEMS WITH POSITION-DEPENDENT EFFECTIVE MASSES ⋮ EXACT SOLUTIONS OF EFFECTIVE-MASS SCHRÖDINGER EQUATIONS ⋮ Energy eigenfunctions for position-dependent mass particles in a new class of molecular Hamiltonians ⋮ A quantum exactly solvable nonlinear oscillator with quasi-harmonic behaviour ⋮ Generalized Korteweg-de Vries equation induced from position-dependent effective mass quantum models and mass-deformed soliton solution through inverse scattering transform ⋮ Torsion effects on a relativistic position-dependent mass system ⋮ Dirac equation for the harmonic scalar and vector potentials and linear plus Coulomb-like tensor potential; the SUSY approach ⋮ PDM creation and annihilation operators of the harmonic oscillators and the emergence of an alternative PDM-Hamiltonian ⋮ Dynamically Orthogonal Runge–Kutta Schemes with Perturbative Retractions for the Dynamical Low-Rank Approximation ⋮ Quantum solvability of a general ordered position dependent mass system: Mathews-Lakshmanan oscillator ⋮ Exceptional orthogonal polynomials and exactly solvable potentials in position dependent mass Schrödinger Hamiltonians ⋮ Quantization of Hamiltonian systems with a position dependent mass: Killing vector fields and Noether momenta approach ⋮ Approximate series solutions of the \(N\)-dimensional position-dependent mass Schrödinger equation ⋮ Coordinate Transformation and Exact Solutions of Schrödinger Equation with Position-Dependent Effective Mass ⋮ A complete set of eigenstates for position-dependent massive particles in a Morse-like scenario ⋮ Analytic solutions, Darboux transformation operators and supersymmetry for a generalized one-dimensional time-dependent Schrödinger equation ⋮ Quantum wave packet revival in two-dimensional circular quantum wells with position-dependent mass ⋮ A singular position-dependent mass particle in an infinite potential well ⋮ Transforming kinks into compactons in the \(O(3)\)-sigma model ⋮ Effective mass Schrödinger equation for exactly solvable class of one-dimensional potentials ⋮ BOUND STATES OF THE KLEIN–GORDON EQUATION FOR WOODS–SAXON POTENTIAL WITH POSITION DEPENDENT MASS ⋮ PT-symmetric solutions of Schrödinger equation with position-dependent mass via point canonical transformation ⋮ Coherent states of position-dependent mass trapped in an infinite square well ⋮ κ-Deformed quantum and classical mechanics for a system with position-dependent effective mass ⋮ DIRAC EQUATION FOR A COULOMB SCALAR, VECTOR AND TENSOR INTERACTION ⋮ $\mathcal {CPT}$ CPT -conserved effective mass Hamiltonians through first and higher order charge operator $\mathcal {C}$C in a supersymmetric framework ⋮ Ordering ambiguity revisited via position dependent mass pseudo-momentum operators ⋮ Exact solutions of the position-dependent mass Schrödinger equation in \(D\) dimensions ⋮ A study of the bound states for square potential wells with position-dependent mass ⋮ Coherent states of position-dependent mass oscillator ⋮ Solutions to position-dependent mass quantum mechanics for a new class of hyperbolic potentials ⋮ A parametric approach to supersymmetric quantum mechanics in the solution of Schrödinger equation ⋮ Exactly solvable potentials for the Schrödinger equation with spatially dependent mass ⋮ Extension of PT-symmetric quantum mechanics to the Dirac theory with position-dependent mass ⋮ Solutions of the spatially-dependent mass Dirac equation with the spin and pseudospin symmetry for the Coulomb-like potential ⋮ Classes of exact Klein-Gordon equations with spatially dependent masses: regularizing the one-dimensional inversely linear potential ⋮ A GENERAL SCHEME FOR THE EFFECTIVE-MASS SCHRÖDINGER EQUATION AND THE GENERATION OF THE ASSOCIATED POTENTIALS ⋮ EFFECTIVE MASS HAMILTONIANS WITH LINEAR TERMS IN THE MOMENTUM: DARBOUX TRANSFORMATIONS AND FORM-PRESERVING TRANSFORMATIONS ⋮ Dirac equation in the presence of Coulomb and linear terms in \((1+1)\) dimensions; the supersymmetric approach ⋮ Relativistic confinement of neutral fermions with partially exactly solvable and exactly solvable PT-symmetric potentials in the presence of position-dependent mass ⋮ DARBOUX TRANSFORMATIONS FOR TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH EFFECTIVE MASS ⋮ Exactly solvable potentials and the bound-state solution of the position-dependent mass Schrödinger equation in \(D\)-dimensional space ⋮ Exact mapping between charge-monopole and position-dependent effective mass systems via Pauli equation ⋮ Mapping Between Charge-Dyon and Position-Dependent Mass Systems* ⋮ Coherent and Squeezed States: Introductory Review of Basic Notions, Properties, and Generalizations ⋮ Variational Method Applied to Schrödinger-Like Equation ⋮ EXACTLY SOLVABLE EFFECTIVE MASS D-DIMENSIONAL SCHRÖDINGER EQUATION FOR PSEUDOHARMONIC AND MODIFIED KRATZER PROBLEMS ⋮ Comparison theorems for the position-dependent mass Schrödinger equation ⋮ Landau quantization for an electric quadrupole moment of position-dependent mass quantum particles interacting with electromagnetic fields ⋮ Removal of ordering ambiguity for a class of position dependent mass quantum systems with an application to the quadratic Liénard type nonlinear oscillators ⋮ Quantum systems with position-dependent mass and spin-orbit interaction via Rashba and Dresselhaus terms ⋮ An exactly solvable Schrödinger equation with finite positive position-dependent effective mass ⋮ Approximate solutions of the Dirac equation for the Rosen–Morse potential including the spin-orbit centrifugal term ⋮ REALITY CONDITION FOR DARBOUX TRANSFORMATIONS OF TIME-DEPENDENT SCHRÖDINGER EQUATIONS WITH EFFECTIVE MASS ⋮ Confined Klein-Gordon oscillators in Minkowski spacetime and a pseudo-Minkowski spacetime with a space-like dislocation: PDM KG-oscillators, isospectrality and invariance ⋮ MORSE POTENTIAL AND ITS RELATIONSHIP WITH THE COULOMB IN A POSITION-DEPENDENT MASS BACKGROUND ⋮ SOLUTION OF THE DIRAC EQUATION WITH POSITION-DEPENDENT MASS IN A COULOMB AND SCALAR FIELDS IN A CONICAL SPACETIME ⋮ AUXILIARY QUANTIZATION CONSTRAINTS ON THE VON ROOS ORDERING-AMBIGUITY AT ZERO BINDING ENERGIES; AZIMUTHALLY SYMMETRIZED CYLINDRICAL COORDINATES ⋮ The relativistic Aharonov–Bohm–Coulomb system with position-dependent mass ⋮ so(2, 1) algebra, local Fermi velocity, and position-dependent mass Dirac equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Green's functions through \(SO(2,1)\) Lie algebra in nonrelativistic quantum mechanics
• Quantum motion in a Paul trap
• Analytical Solutions for Velocity-Dependent Nuclear Potentials
• Hamiltonian Operators via Feynman Path Integrals
• Electrons in Perturbed Periodic Lattices
• Motion of Electrons and Holes in Perturbed Periodic Fields