A Numerical Treatment of Energy Eigenvalues of Harmonic Oscillators\n Perturbed by a Rational Function

2016/10/12 by Philippe Gaudreau, Gaudreau, Philippe, Hassan Safouhi +1
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1610.03613

openalex publication_date 2016/10/12 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In the present contribution, we apply the double exponential Sinc-collocation\nmethod (DESCM) to the one-dimensional time independent Schr "odinger equation\nfor a class of rational potentials of the form V(x) =p(x)/q(x). This\nalgorithm is based on the discretization of the Hamiltonian of the\nSchr "odinger equation using Sinc expansions. This discretization results in a\ngeneralized eigenvalue problem where the eigenvalues correspond to\napproximations of the energy values of the corresponding Hamiltonian. A\nsystematic numerical study is conducted, beginning with test potentials with\nknown eigenvalues and moving to rational potentials of increasing degree.\n

Citations

• A Perspective on Constructive Quantum Field Theory

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