Journal of the Korean Physical Society

Korean Physical Society (한국물리학회)
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Solving Time-dependent Schrödinger Equation Using Gaussian Wave Packet Dynamics

  • Lee, Min-Ho (School of Liberal Arts and Teacher Training, Kumoh National Institute of Technology) ;
  • Byun, Chang Woo (School of Liberal Arts and Teacher Training, Kumoh National Institute of Technology) ;
  • Choi, Nark Nyul (School of Liberal Arts and Teacher Training, Kumoh National Institute of Technology) ;
  • Kim, Dae-Soung (Department of Global Education, Gyeonggi College of Science and Technology)
  • Received : 2018.08.28
  • Published : 2018.11.15
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Abstract

Using the thawed Gaussian wave packets [E. J. Heller, J. Chem. Phys. 62, 1544 (1975)] and the adaptive reinitialization technique employing the frame operator [L. M. Andersson et al., J. Phys. A: Math. Gen. 35, 7787 (2002)], a trajectory-based Gaussian wave packet method is introduced that can be applied to scattering and time-dependent problems. This method does not require either the numerical multidimensional integrals for potential operators or the inversion of nearly-singular matrices representing the overlap of overcomplete Gaussian basis functions. We demonstrate a possibility that the method can be a promising candidate for the time-dependent $Schr{\ddot{o}}dinger$ equation solver by applying to tunneling, high-order harmonic generation, and above-threshold ionization problems in one-dimensional model systems. Although the efficiency of the method is confirmed in one-dimensional systems, it can be easily extended to higher dimensional systems.

Keywords

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