International Journal of Quantum Chemistry

Volume 45, Issue 6 pp. 637-647

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Resolution of Schrödinger's equation for a scattering problem by a finite-element method

Th. Laloyaux,

Th. Laloyaux

Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium

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J.-P. Vigneron,

J.-P. Vigneron

Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium

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Ph. Lambin,

Ph. Lambin

Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium

Research Associate of the Belgian National Fund for Scientific Research.

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I. Derycke,

I. Derycke

Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium

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A. A. Lucas,

A. A. Lucas

Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium

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Th. Laloyaux,

Th. Laloyaux

Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium

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J.-P. Vigneron,

J.-P. Vigneron

Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium

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Ph. Lambin,

Ph. Lambin

Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium

Research Associate of the Belgian National Fund for Scientific Research.

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I. Derycke,

I. Derycke

Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium

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A. A. Lucas,

A. A. Lucas

Facultés Universitaires Notre-Dame de la Paix, 61, rue de Bruxelles, B-5000 Namur, Belgium

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First published: 1993

https://doi.org/10.1002/qua.560450613

Citations: 2

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Abstract

We present a new numerical method for solving the Schrödinger equation in the case of scattering or tunneling states. As an example, we study a model of the scanning tunneling microscope. The method uses a finite-element approximation of the wave function in the region of the scattering potential. From the wave function that we obtain, we derive the tunnel current density. © 1993 John Wiley & Sons, Inc.

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Volume45, Issue6

1993

Pages 637-647

Resolution of Schrödinger's equation for a scattering problem by a finite-element method

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Resolution of Schrödinger's equation for a scattering problem by a finite-element method

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