Double exponential sinc-collocation method for solving the energy eigenvalues of harmonic oscillators perturbed by a rational function

作者：Gaudreau Philippe; Safouhi Hassan^*

来源：Journal of Mathematical Physics, 2017, 58(10): 101509.

DOI：10.1063/1.5004974

We show that the double exponential sinc-collocation method provides an efficient uniformly accurate solution to the one-dimensional time independent Schrodinger equation for a general class of rational potentials of the form V (x) = p(x)/q(x). The derived algorithm is based on the discretization of the Hamiltonian of the Schrodinger equation using sinc expansions. This discretization results in a generalized eigenvalue problem, the eigenvalues of which correspond to approximations of the energy values of the starting Hamiltonian. Asystematic numerical study is conducted, beginning with test potentials with known eigenvalues and moving to rational potentials of increasing degree. Published by AIP Publishing.

• 出版日期2017-10