Inverse problem of quadratic time-dependent Hamiltonians

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

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.

Keywords: quadratic time-dependent Hamiltonians analytical solution inverse method

Received: 03 February 2015
Revised: 16 March 2015
Accepted manuscript online:

PACS:	03.65.Ca	(Formalism)
	03.65.Db	(Functional analytical methods)
	03.65.Fd	(Algebraic methods)

Fund: 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).

Corresponding Authors: Di Bing
E-mail: dibing@hebtu.edu.cn

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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 2015 Chin. Phys. B 24 080301

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