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Volume 2, Issue 1
Conservative Local Discontinuous Galerkin Methods for Time Dependent Schrödinger Equation

T. Lu, W. Cai & P. Zhang

Int. J. Numer. Anal. Mod., 2 (2005), pp. 75-84.

Published online: 2005-02

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  • Abstract

This paper presents a high order local discontinuous Galerkin time-domain method for solving time dependent Schrödinger equations. After rewriting the Schrödinger equation in terms of a first order system of equations, a numerical flux is constructed to preserve the conservative property for the density of the particle described. Numerical results for a model square potential scattering problem is included to demonstrate the high order accuracy of the proposed numerical method.

  • Keywords

Local discontinuous Galerkin (LDG) method, Schrödinger equation, quantum structures.

  • AMS Subject Headings

65N30, 47N40, 81Q05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-2-75, author = {T. Lu, W. Cai and P. Zhang}, title = {Conservative Local Discontinuous Galerkin Methods for Time Dependent Schrödinger Equation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {1}, pages = {75--84}, abstract = {

This paper presents a high order local discontinuous Galerkin time-domain method for solving time dependent Schrödinger equations. After rewriting the Schrödinger equation in terms of a first order system of equations, a numerical flux is constructed to preserve the conservative property for the density of the particle described. Numerical results for a model square potential scattering problem is included to demonstrate the high order accuracy of the proposed numerical method.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/921.html} }
TY - JOUR T1 - Conservative Local Discontinuous Galerkin Methods for Time Dependent Schrödinger Equation AU - T. Lu, W. Cai & P. Zhang JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 75 EP - 84 PY - 2005 DA - 2005/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/921.html KW - Local discontinuous Galerkin (LDG) method, Schrödinger equation, quantum structures. AB -

This paper presents a high order local discontinuous Galerkin time-domain method for solving time dependent Schrödinger equations. After rewriting the Schrödinger equation in terms of a first order system of equations, a numerical flux is constructed to preserve the conservative property for the density of the particle described. Numerical results for a model square potential scattering problem is included to demonstrate the high order accuracy of the proposed numerical method.

T. Lu, W. Cai and P. Zhang. (2005). Conservative Local Discontinuous Galerkin Methods for Time Dependent Schrödinger Equation. International Journal of Numerical Analysis and Modeling. 2 (1). 75-84. doi:
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