Analytical Lanczos method: quantum eigenstates of anharmonic oscillators in one or more dimensions

Published: 1 January 1994| Version 1 | DOI: 10.17632/c4hp5gjyjm.1
Matjaž Kaluža


Abstract The analytical Lanczos method is a simple method to calculate the eigenstates of quantum-mechanical Hamiltonians of systems with several degrees of freedom. High precision eigenvalues and eigenfunctions are obtained for the anharmonic oscillator, and for two, three and four coupled anharmonic oscillators, by diagonalizing small tridiagonal matrices. Title of program: LANCZOS-A Catalogue Id: ACTR_v1_0 Nature of problem A number of problems in chemistry, atomic, nuclear, particle and statistical physics can be reduced to accurate evaluation of eigenspectra and eigenfunctions of an anharmonic oscillator or of a system of coupled anharmonic oscillators. In this paper we present a number of accurate eigensolutions for an example of a sextic anharmonic oscillator in one dimension where up to 88 digits accuracy is achieved, and for examples of two, three and four coupled one-dimensional sextic anharmonic oscillators ... Versions of this program held in the CPC repository in Mendeley Data ACTR_v1_0; LANCZOS-A; 10.1016/0010-4655(94)90186-4 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)



Computational Physics, Computer Algebra System, Computational Method