No abstract

No abstract

No abstract

A quantum anharmonic oscillator is defined by the Hamiltonian H = − d 2 dx 2 + V (x), where the potential is given byUsing the Sinc collocation method combined with the double exponential transformation, we develop a method to efficiently compute highly accurate approximations of energy eigenvalues for anharmonic oscillators. Convergence properties of the proposed method are presented. Using the principle of minimal sensitivity, we introduce an alternate expression for the mesh size for the Sinc collocation method which improves considerably the accuracy in computing eigenvalues for potentials with multiple wells.We apply our method to a number of potentials including potentials with multiple wells. The numerical results section clearly illustrates the high efficiency and accuracy of the proposed method. All our codes are written using the programming language Julia and are available upon request.

Density functional theory requires precise numerical values for three-Ž . center nuclear attraction integrals, best obtained over Slater-type orbitals STOs . Efficient evaluation of three-center nuclear attraction integrals over STOs to predetermined accuracy is made possible by applying the nonlinear D and D transformations. These methods are implemented in Fortran subroutines. This work shows how the conditions of applicability for these transformations are readily proven to be satisfied using the Axiom symbolic computation system. Axiom also provides exact values of the integrals for comparison. Their evaluation by standard numerical quadrature methods Ž . Gauss᎐Laguerre , proves inadequate: Certain parameters lead to inaccurate values for the integrals, whereas the transformed integrals are highly accurate and rapidly evaluated.

No abstract

No abstract

No abstract