Analysis of the Three-dimensional time-dependent Schrödinger equation by the meshless local Petrov- Galerkin method

Document Type : Full length research Paper

Authors

1 Department of Mechanical Engineering, Sirjan University of Technology

2 Faculty of Physics, University of Shahid bahonar Kerman.

Abstract

In this paper, the meshless local Petrov-Galerkin (MLPG) method is presented for the numerical solution of the three-dimensional time-dependent Schrödinger equation. The method is based on the local weak form and the moving least squares (MLS) approximation. In this paper, the Heaviside step function is regarded as the test function. Local sub-domains are also considered as cubic shapes. In order to satisfy the essential boundary conditions, the penalty parameter technique is implemented due to the MLS approximation can’t satisfy Kroniker delta function property. The forward finite difference method is used to decompose the time expression of Schrödinger equations. Moreover, the MLPG results of the problem are compared with those obtained by an exact analytical solution which shows the efficiency and accuracy of this method.

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References

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Journal of Research on Many-body Systems
Volume 8, Issue 17
September 2018
Pages 51-58

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History

  • Receive Date: 25 July 2017
  • Revise Date: 15 February 2018
  • Accept Date: 23 April 2018

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