An accurate method for numerical calculations in quantum mechanics

An. accurate method for numerical calculations of matrix elements and for solving the eigenvalue problem in quantum mechanics is presented. Methods for numerical interpolation, differentiation and integration provide 15-digit accuracy with double-precision arithmetic operations. A method for solution of the eigenvalue problem of an ordinary differential equation by using discretization and matrix eigenvalue methods provides 13- to 15-digit accuracy. The efficiency of the proposed methods is demonstrated by the applications to bound states for the linear harmonic oscillator, anharmonic oscillators, the Morse potential and the modified Poschl-Teller potential.