Solving differential aquations in quantum mechanics using sinc functions in one and two dimensions, employing Python and Numpy
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Authors
Ezenwachukwu, Obiageli Lovenda
Issue Date
2021-10-07
Type
Dissertation
Language
en
Keywords
Sinc functions , Numerical methods , Python , Numpy , Scipy , Morse potential , Eigenvalue problem , Computational physics , Cusp factor , Hydrogen molecular ion , Least square fits
Alternative Title
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.