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Accurate boundary treatment for time-dependent 3D Schrödinger equation under Spherical coordinates

Author

Listed:
  • Linfeng Zhang

    (School of Transportation, Jilin University, Changchun 130012, P. R. China†University of Wisconsin-Madison, 1212 Engineering Hall, 1415 Engineering Drive, Madison, WI 53706, USA)

  • Hongfei Jia

    (School of Transportation, Jilin University, Changchun 130012, P. R. China)

  • Lei Bian

    (School of Transportation, Jilin University, Changchun 130012, P. R. China‡Travelsky Mobile Technology Limited, Beijing 100087, P. R. China)

  • Bin Ran

    (#x2020;University of Wisconsin-Madison, 1212 Engineering Hall, 1415 Engineering Drive, Madison, WI 53706, USA)

Abstract

We propose a novel local boundary condition for three-dimensional Schrödinger equation under spherical coordinates. It is based on the approximate linear relationship among the Bessel functions from a free one-dimensional Schrödinger equation. With a variable transform, the novel boundary condition is a simple form of some ordinary differential equations, which relate the grid point near the numerical boundaries. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary conditions.

Suggested Citation

  • Linfeng Zhang & Hongfei Jia & Lei Bian & Bin Ran, 2020. "Accurate boundary treatment for time-dependent 3D Schrödinger equation under Spherical coordinates," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-13, January.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:01:n:s0129183120500151
    DOI: 10.1142/S0129183120500151
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