Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions
arXiv:0705.2577 · doi:10.3842/SIGMA.2007.067
Abstract
An exactly solvable position-dependent mass Schrödinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together with a realization in terms of deformed parafermionic oscillator operators. In this process, the importance of supplementing algebraic considerations with a proper treatment of boundary conditions for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived. This example emphasizes the interest of a quadratic algebra approach to position-dependent mass Schrödinger equations.
Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
References in corpus (10)
- Supersymmetry and Quantum Mechanics
- Effective Mass of One 4he Atom in Liquid 3he
- Quadratic Poisson algebras for two dimensional classical superintegrable systems and quadratic associative algebras for quantum superintegrable systems
- Deformed oscillator algebras for two dimensional quantum superintegrable systems
- Quantum particles trapped in a position-dependent mass barrier; a d-dimensional recipe
- d-Dimensional generalization of the point canonical transformation for a quantum particle with position-dependent mass
- Superintegrability on the two dimensional hyperboloid II
- Classification of quantum superintegrable systems with quadratic integrals on two dimensional manifolds
- Nondegenerate 3D complex Euclidean superintegrable systems and algebraic varieties
- A state with negative binding energy induced by coherent transport in a quantum wire
Cited by in corpus (17)
- Classical and Quantum Superintegrability with Applications
- AdS perturbations, isometries, selection rules and the Higgs oscillator
- Algebraic Calculation of the Energy Eigenvalues for the Nondegenerate Three-Dimensional Kepler-Coulomb Potential
- Superintegrable systems with position dependent mass
- Models of Quadratic Algebras Generated by Superintegrable Systems in 2D
- Models for Quadratic Algebras Associated with Second Order Superintegrable Systems in 2D
- On realizations of polynomial algebras with three generators via deformed oscillator algebras
- Group classification of Schrödinger equations with position dependent mass
- Hidden symmetries of the Higgs oscillator and the conformal algebra
- The general Racah algebra as the symmetry algebra of generic systems on pseudo--spheres
- Symmetries of the Schroedinger-Pauli equation for neutral particles
- Exact solvability of PDM systems with extended Lie symmetries
- Generalized quantum Zernike Hamiltonians: Polynomial Higgs-type algebras and algebraic derivation of the spectrum
- Generalized quadratic commutator algebras of PBW-type
- Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras
- Representations of quadratic Heisenberg-Weyl algebras and polynomials in the fourth Painlevé transcendent
- Symmetries and Supersymmetries of Generalized Schrödinger equations