EJIIM for the stationary Schrödinger equations with delta potential wells

摘要

We investigate the bound state problems for the 1D stationary Schrödinger equations with a class of singular potentials, i.e. the delta potential wells, by using the explicit jump immersed interface method (EJIIM). Either in the single-delta case or in the double-delta case, numerical results show the feasibility, efficiency and convergence of EJIIM with applications to the eigenvalue problems, just as to numerous boundary value and initial-boundary value differential equations. Comparisons with Peskin’s IB method reveal the superiority of EJIIM in calculating the bound eigenfunctions and particularly the corresponding eigenvalues for the stationary Schrödinger equations.