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


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

Notice: Undefined variable: pac in /var/www/html/issue/abstract/readabs.php on line 164
Key words: Schrodinger equation, numerical scheme, resonant tunneling, multi-mode approximation, high dimension.

*Corresponding author.
Email: (H. Wu)

The Global Science Journal