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

Linfeng Zhang, Hongfei Jia, Lei Bian and Bin Ran ()
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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

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 01, 1-13

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.

Keywords: Three-dimensional Schrödinger equation; spherical coordinates; boundary conditions (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0129183120500151

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