Some applications of perturbation theory to numerical integration methods for the Schrödinger equation

✍ Scribed by J. Killingbeck

• Publisher: Elsevier Science
• Year: 1979
• Tongue: English
• Weight: 336 KB
• Volume: 18
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(79)90114-0

✦ Synopsis

By using the methods of perturbation theory it is possible to construct simple formulae for the numerical integration of the Schrodinger equation, and also to calculate expectation values solely by means of simple eigenvalue calculations.

1. The basic theory may be a multiplicative operator instead of a differential operator). In the present work we wish to point out how some In general A is not unique, it can be adjusted by basic ideas of first order perturbation theory can be adding to it any operator which gives a zero expectaused in connection with methods of direct numerical tion value for the unperturbed wavefunction. Such integration to give accurate eigenvalues for the one-operators can be found by using the theory of hyperdimensional Schrodinger equation. We take the equa-virial relations [2]; if H denotes the Hamiltonian tion in the form operator in eq. ( 1), then any operator B leads to a -D 2 I + v= 11 \ commutator [H,B] which has zero expectation value