Inverse problem of quadratic time-dependent Hamiltonians  

作　　者：郭光杰 孟艳 常虹 段会增 邸冰 

机构地区：[1]Department of Physics and Electromagnetic Transport Materials Laboratory, Xingtai University [2]College of Physics and Hebei Advanced Thin Films Laboratory, Hebei Normal University

出　　处：《Chinese Physics B》2015年第8期159-165,共7页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.11347171);the Natural Science Foundation of Hebei Province of China(Grant No.A2012108003);the Key Project of Educational Commission of Hebei Province of China(Grant No.ZD2014052)

摘　　要：Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wavepacket 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 timedependent periodic harmonic oscillator, the Berry phase is obtained exactly.Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wavepacket 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 timedependent periodic harmonic oscillator, the Berry phase is obtained exactly.

关 键 词：quadratic time-dependent Hamiltonians analytical solution inverse method 

分 类 号：O413.1[理学—理论物理]