General requirements for the use of finite basis sets that do not satisfy the boundary conditions

Publisher Website
Google Scholar
Abstract
The authors present a method for using basis functions which do not satisfy the boundary conditions for confined systems in which the boundary surface is of arbitrary shape and complexity. They show that the existence of a variational solution which does satisfy the boundary conditions is possible only if the basis set is linearly dependent on the boundary surface. This criterion also suggests two methods of approximating solutions when this condition is not satisfied. The variational solutions are shown to be the orthogonal set of eigenfunctions of a projected Hamiltonian. The projected subspace is the set of null eigenvectors of the boundary surface overlap matrix. The method is applied to the problem of a hydrogen atom in an infinitely strong spherical box displaced from the centre of the well. Results are compared with those of previous authors.

This publication has 2 references indexed in Scilit: