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

• DOI: 10.48550/arxiv.1610.03613
• Publication Date: 2016-01-01
• Authors: Philippe Gaudreau; Hassan Safouhi
• Keywords: Sinc function; Hamiltonian (control theory); Eigenfunction; Collocation (remote sensing)

In the present contribution, we apply double exponential Sinc-collocation method (DESCM) to one-dimensional time independent Schr\"odinger equation for a class of rational potentials form $V(x) =p(x)/q(x)$. This algorithm is based on discretization Hamiltonian using Sinc expansions. results in generalized eigenvalue problem where eigenvalues correspond approximations energy values corresponding Hamiltonian. A systematic numerical study conducted, beginning with test known and moving increasing degree.