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Numerical and perturbation theoretic methods for the solution of the Schrödinger equation

Galicia Martín del Campo, Susana


Susana Galicia Martín del Campo


In the present work we present a numerical and perturbation theoretic approach to the solution of the one-particle Schrödinger equation. The
numerical methods developed can be used to find energy eigenvalues for one-dimensional problems as well as for radial ones. Expectation values are determined by an approach based on eigenvalue calculations, without the explicit use of wave functions.

Hypervirial and Hellmann-Feynman theorems are used to obtain perturbation series to high order for polynomial type radial perturbations of the hydrogen atom. One such perturbation leads to an apparently new phenomenon in Rayleigh-Schrödinger perturbation theory.

Wynn's algorithm is used to get Padé approximants for the perturbation series. The series for the energy and for the quantities <rᴺ> are treated, and both types of series can be found using the hypervirial method.

Several applications of the numerical techniques are given; it is emphasized that theoretical manipulations are needed to transform the problem to an appropriate numerical form. It is demonstrated that a slight modification in the numerical techniques developed permits treatment of quasi-bound states as well as bound states. It is also shown how to calculate a local quantity Ψ(O), using energy calculations, and how to reduce the problem of treating angular terms in the quadratic Zeeman effect problem to a radial integration problem.


Galicia Martín del Campo, S. (1980). Numerical and perturbation theoretic methods for the solution of the Schrödinger equation. (Thesis). University of Hull. Retrieved from

Thesis Type Thesis
Deposit Date Mar 8, 2016
Publicly Available Date Feb 23, 2023
Keywords Physics
Public URL
Additional Information Department of Physics, The University of Hull
Award Date Sep 1, 1980


Thesis (4 Mb)

Copyright Statement
© 1980 Galicia Martín del Campo, Susana. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright holder.

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