Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation
R. D. Mota, D. Ojeda-Guillén
Abstract
In this paper, we introduce a generalization of the Dunkl derivative with two parameters to study the Schrödinger equation in Cartesian and polar coordinates in two dimensions. The eigenfunctions and the energy spectrum for the harmonic oscillator and the Coulomb problem are derived in an analytical way and it is shown that our results are properly reduced to those previously reported for the Dunkl derivative with a single parameter.
Topics & Concepts
PhysicsEigenfunctionCartesian coordinate systemGeneralizationHarmonic oscillatorDerivative (finance)Polar coordinate systemMathematical physicsSchrödinger equationSecond derivativeSpectrum (functional analysis)Mathematical analysisQuantum mechanicsEigenvalues and eigenvectorsGeometryMathematicsEconomicsFinancial economicsQuantum Mechanics and Non-Hermitian PhysicsMathematical Analysis and Transform MethodsQuantum chaos and dynamical systems