Solving differential aquations in quantum mechanics using sinc functions in one and two dimensions, employing Python and Numpy

Abstract

In this contribution the sinc basis functions are used to numerically solve the Schrödinger equation in one and two dimensions for a number of potentials. The calculations are done using the Python and Numpy modules. Conver gence is found to be fast for the harmonic oscillator. For the Morse potential it agrees with the theoretically expected behaviour. In the two dimensional case code optimization leads to a large speed-up. We also present the results of calculations for the ground state energy of the hydrogen molecular ion em ploying Sinc functions as a basis set. Modifications are required to make the basis functions suitable for calculating the ground state energy of the hydro gen molecular ion with the application of the cusp factor formalism . Finally the resulting energies are investigated as a function of the number of basis functions and double-logarithmic fits are performed.