2008/08/28 by Vanyolos, Andras, Varga, Gabor
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.0808.3976
We study numerically the Coulomb interacting two-particle stationary states of the Schrödinger equation, where the particles are confined in a two-dimensional infinite square well. Inside the domain the particles are subjected to a steeply increasing isotropic harmonic potential, resembling that in a nucleus. For these circumstances we have developed a fully discretized finite difference method of the Numerov-type that approximates the four-dimensional Laplace operator, and thus the whole Schrödinger equation, with a local truncation error of O(h6), with h being the uniform step size. The method is built on a 89-point central difference scheme in the four-dimensional grid. As expected from the general theorem by Keller [Num. Math. 7, 412 (1965)], the error of eigenvalues so obtained are found to be the same order of magnitude which we have proved analytically as well.