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http://dx.doi.org/10.3938/jkps.73.1269

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)
Publication Information
Journal of the Korean Physical Society / v.73, no.9, 2018 , pp. 1269-1278 More about this Journal
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
Gaussian Gabor frame; Gaussian wave packet; Tunneling; HHG; ATI;
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