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Time-dependent variational approach to solve multi-dimensional time-dependent Schrödinger equation |
| Mingrui He(何明睿)1,†, Zhe Wang(王哲)1, Lufeng Yao(姚陆锋)1, and Yang Li(李洋)2,‡ |
1 Department of Basic Courses, Naval University of Engineering, Wuhan 430033, China;
2 Key Laboratory for Laser Plasmas(Ministry of Education) and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China |
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Abstract We present an efficient approach to solve multi-dimensional time-dependent Schrödinger equation (TDSE) in an intense laser field. In this approach, each spatial degree of freedom is treated as a distinguishable quasi-particle. The non-separable Coulomb potential is regarded as a two-body operator between different quasi-particles. The time-dependent variational principle is used to derive the equations of motion. Then the high-order multi-dimensional problem is broken down into several lower-order coupled equations, which can be efficiently solved. As a demonstration, we apply this method to solve the two-dimensional TDSE. The accuracy is tested by comparing the direct solutions of TDSE using several examples such as the strong-field ionization and the high harmonic generation. The results show that the present method is much more computationally efficient than the conventional one without sacrificing accuracy. The present method can be straightforwardly extended to three-dimensional problems. Our study provides a flexible method to investigate the laser-atom interaction in the nonperturbative regime.
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Received: 26 April 2023
Revised: 03 August 2023
Accepted manuscript online: 11 August 2023
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PACS:
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42.65.Ky
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(Frequency conversion; harmonic generation, including higher-order harmonic generation)
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42.65.Re
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(Ultrafast processes; optical pulse generation and pulse compression)
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32.80.Fb
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(Photoionization of atoms and ions)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant Nos.12204545 and 12274294) and the Program for NUE independent research and development. |
Corresponding Authors:
Mingrui He, Yang Li
E-mail: hmr_emma@163.com;liyang22@sjtu.edu.cn
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Cite this article:
Mingrui He(何明睿), Zhe Wang(王哲), Lufeng Yao(姚陆锋), and Yang Li(李洋) Time-dependent variational approach to solve multi-dimensional time-dependent Schrödinger equation 2023 Chin. Phys. B 32 124206
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