Inverse problem of quadratic time-dependent Hamiltonians

doi:10.1088/1674-1056/24/8/080301

中国物理B ›› 2015, Vol. 24 ›› Issue (8): 80301-080301.doi: 10.1088/1674-1056/24/8/080301

Inverse problem of quadratic time-dependent Hamiltonians

郭光杰^a, 孟艳^a, 常虹^b, 段会增^a, 邸冰^b

a Department of Physics and Electromagnetic Transport Materials Laboratory, Xingtai University, Xingtai 054001, China;
b College of Physics and Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang 050024, China

收稿日期:2015-02-03 修回日期:2015-03-16 出版日期:2015-08-05 发布日期:2015-08-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11347171), the Natural Science Foundation of Hebei Province of China (Grant No. A2012108003), and the Key Project of Educational Commission of Hebei Province of China (Grant No. ZD2014052).

Inverse problem of quadratic time-dependent Hamiltonians

Guo Guang-Jie (郭光杰)^a, Meng Yan (孟艳)^a, Chang Hong (常虹)^b, Duan Hui-Zeng (段会增)^a, Di Bing (邸冰)^b

a Department of Physics and Electromagnetic Transport Materials Laboratory, Xingtai University, Xingtai 054001, China;
b College of Physics and Hebei Advanced Thin Films Laboratory, Hebei Normal University, Shijiazhuang 050024, China

Received:2015-02-03 Revised:2015-03-16 Online:2015-08-05 Published:2015-08-05
Contact: Di Bing E-mail:dibing@hebtu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11347171), the Natural Science Foundation of Hebei Province of China (Grant No. A2012108003), and the Key Project of Educational Commission of Hebei Province of China (Grant No. ZD2014052).

摘要/Abstract

摘要： Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly.

关键词: quadratic time-dependent Hamiltonians, analytical solution, inverse method

Abstract: Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wave-packet obeying the quadratic time-dependent Hamiltonian (QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific time-dependent periodic harmonic oscillator, the Berry phase is obtained exactly.

Key words: quadratic time-dependent Hamiltonians, analytical solution, inverse method

中图分类号: (Formalism)

03.65.Ca

03.65.Db (Functional analytical methods) 03.65.Fd (Algebraic methods)

郭光杰, 孟艳, 常虹, 段会增, 邸冰. Inverse problem of quadratic time-dependent Hamiltonians[J]. 中国物理B, 2015, 24(8): 80301-080301.

Guo Guang-Jie (郭光杰), Meng Yan (孟艳), Chang Hong (常虹), Duan Hui-Zeng (段会增), Di Bing (邸冰). Inverse problem of quadratic time-dependent Hamiltonians[J]. Chin. Phys. B, 2015, 24(8): 80301-080301.

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Inverse problem of quadratic time-dependent Hamiltonians

Inverse problem of quadratic time-dependent Hamiltonians

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