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Solving Time-dependent Schrödinger Equation Using Gaussian Wave Packet Dynamics

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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 Schrödinger 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.

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Authors and Affiliations

  1. School of Liberal Arts and Teacher Training, Kumoh National Institute of Technology, Gumi, 39177, Korea

    Min-Ho Lee, Chang Woo Byun & Nark Nyul Choi

  2. Department of Global Education, Gyeonggi College of Science and Technology, Siheung, 15073, Korea

    Dae-Soung Kim

Authors
  1. Min-Ho Lee
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  2. Chang Woo Byun
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  3. Nark Nyul Choi
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  4. Dae-Soung Kim
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Correspondence to Min-Ho Lee.

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Lee, MH., Byun, C.W., Choi, N.N. et al. Solving Time-dependent Schrödinger Equation Using Gaussian Wave Packet Dynamics. J. Korean Phys. Soc. 73, 1269–1278 (2018). https://doi.org/10.3938/jkps.73.1269

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