Premium
Accurate computation of the energy spectrum for potentials with multiminima
Author(s) -
Taşeli Hasan
Publication year - 1993
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560460207
Subject(s) - eigenvalues and eigenvectors , boundary value problem , maxima and minima , computation , mathematical analysis , degenerate energy levels , truncation (statistics) , mathematics , basis function , convergence (economics) , spectrum (functional analysis) , dirichlet boundary condition , polynomial , physics , quantum mechanics , algorithm , statistics , economics , economic growth
The eigenvalues of the Schrödinger equation with a polynomial potential are calculated accurately by means of the Rayleigh–Ritz variational method and a basis set of functions satisfying Dirichlet boundary conditions. The method is applied to the well potentials having one, two, and three minima. It is shown, in the entire range of coupling constants, that the basis set of trigonometric functions has the capability of yeilding the energy spectra of unbounded problems without any loss of convergence providing that the boundary value α remains greater than a critical value α cr . Only the computation of the nearly degenerate states of multiwell oscillators requires dealing with a relatively large truncation order. © 1993 John Wiley & Sons, Inc.