Commun. Comput. Phys., 10 (2011), pp. 882-898.


A Generalized Stationary Algorithm for Resonant Tunneling: Multi-Mode Approximation and High Dimension

Naoufel Ben Abdallah 1, Hao Wu 2*

1 It is so sad that the author has passed away.
2 Department of Mathematical Sciences, Tsinghua University, Beijing, 10084, China; and Institut de Mathematiques de Toulouse, Universite Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France.

Received 4 June 2010; Accepted (in revised version) 13 October 2010
Available online 13 June 2011
doi:10.4208/cicp.040610.131010a

Abstract

The multi-mode approximation is presented to compute the interior wave function of Schrodinger equation. This idea is necessary to handle the multi-barrier and high dimensional resonant tunneling problems where multiple eigenvalues are considered. The accuracy and efficiency of this algorithm is demonstrated via several numerical examples.

AMS subject classifications: 35C99, 65N99, 81Q05

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Key words: Schrodinger equation, numerical scheme, resonant tunneling, multi-mode approximation, high dimension.

*Corresponding author.
Email: hwu@tsinghua.edu.cn (H. Wu)
 

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