One-dimensional problems: bound and unbound states

Pedro Miguel Echenique

Şaki̇r Erkoç

Before going further to discuss the one–dimensional problems in quantum mechanics, let us first describe the general properties of the one–dimensional Schrödinger equation.

J. D. Kelley, Jacob J. Leventhal

Hasan Taşeli, R. Eid

The eigenvalue problem in of Schrödinger operators with a polynomial perturbation has been replaced by one corresponding to the system confined in a box with impenetrable walls. It is shown that the Dirichlet and the von Neumann problems in generate upper and lower bounds, respectively, to the eigenvalues of the unbounded system. To illustrate the method, rapidly converging two-sided bounds for the energy levels of two- and three-well oscillators are presented, using simple trigonometric basis functions.

S. Brandt, Hans Dieter Dahmen, Tilo Stroh

Francisco Marcelo Fernández

We develop an approach for the treatment of one--dimensional bounded quantum--mechanical models by straightforward modification of a successful method for unbounded ones. We apply the new approach to a simple example and show that it provides solutions to both the bounded and unbounded type of models simultaneously