d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass

Abstract

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrodinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Poschl-Teller and Hulthen potentials are used as reference potentials to obtain exact energy eigenvalues and eigenfunctions for target potentials at different position-dependent mass settings.

14 pages, no figures, to appear in J. Phys. A: Math. Gen

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• A singular position-dependent mass particle in an infinite potential well
• Position-dependent mass, finite-gap systems, and supersymmetry
• (1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric
• Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions
• Algebraic solutions of shape-invariant position-dependent effective mass systems
• Spectrum generating algebras for position-dependent mass oscillator Schrodinger equations
• Non-Hermitian von Roos Hamiltonian's $\eta$-weak-pseudo-Hermiticity, isospectrality and exact solvability
• Analytical Solutions of Klein-Gordon Equation with Position-Dependent Mass for q-Parameter Poschl-Teller potential
• Radial power-law position-dependent mass; Cylindrical coordinates, separability, and spectral signatures
• Coherent states of nonlinear oscillators with position-dependent mass: the temporal stability and fractional revivals
• First-order intertwining operators with position dependent mass and $\eta$- weak-psuedo-Hermiticity generators
• Isochronous $n$-dimensional nonlinear PDM-oscillators: linearizability, invariance and exact solvability
• Remarks on the Solution of the Position Dependent Mass (PDM) Schrödinger Equation
• Position-dependent mass models and their nonlinear characterization
• Energy-levels crossing and radial Dirac equation: Supersymmetry and quasi-parity spectral signatures
• Oscillator-Morse-Coulomb mappings and algebras for constant or position-dependent mass
• Classical and quantum quasi-free position dependent mass; Pöschl-Teller and ordering-ambiguity
• Position-dependent-mass; Cylindrical coordinates, separability, exact solvability, and PT-symmetry
• Exact Solutions of the Schrödinger Equation with position-dependent effective mass via general point canonical transformation
• A quasi-free position-dependent-mass jump and self-scattering correspondence
• Photonic Modes in Twisted Graphene Nanoribbons
• A complete set of eigenstates for position-dependent massive particles in a Morse-like scenario
• Deformation of the Heisenberg-Weyl algebra and the Lie superalgebra $\mathfrak{osp}\left(1|2\right)$: exact solution for the quantum harmonic oscillator with a position-dependent mass
• Mapping of Two-Dimensional Schrödinger Equation under the Point Transformation
• Flatland Position-Dependent-Mass: Polar Coordinates, Separability and Exact Solvability