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Chin. Phys. B, 2015, Vol. 24(8): 080301    DOI: 10.1088/1674-1056/24/8/080301
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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
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

Cite this article: 

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

[1] Schrödinger E 1926 Naturwissenschaften 14 664
[2] Wolfgang P 1990 Rev. Mod. Phys. 62 531
[3] Dodonav V V and Man'ko V I 1970 Phys. Rev. A 20 550
[4] Caldirola P 1983 Nuovo Cimento B 77 241
[5] Agarwal G S and Kumar S A 1991 Phys. Rev. Lett. 67 3665
[6] Feng M and Wang K 1995 Phys. Lett. A 197 135
[7] Delgado F, Mielnik C B and Reyes M A 1998 Phys. Lett. A 237 359
[8] Lu P and Wang S J 2009 Acta Phys. Sin. 58 5955 (in Chinese)
[9] Zhang Y Q, Tan L, Zhu Z H and Liu L W 2010 Chin. Phys. B 19 033202
[10] Tan L, Zhang Y Q and Zhu Z H 2011 Chin. Phys. B 20 070303
[11] Lewis H R Jr 1967 Phys. Rev. Lett. 18 510
[12] Lewis H R Jr and Riesenfeld W B 1968 J. Math. Phys. 9 1976
[13] Guasti M F and Gil-Villegas A 2002 Phys. Lett. A 292 243
[14] Guasti M F and Moya-Cessa H 2003 J. Phys. A: Math. Gen. 36 2069
[15] Wang S J, Li F L and Weiguny A 1993 Phys. Lett. A 180 189
[16] Wang S J, Zuo W, Weiguny A and Li F L 1994 Phys. Lett. A 196 7
[17] Baskoutas S, Jannusis A and Mignani R 1992 Phys. Lett. A 164 17
[18] Yeon K H, Lee K K, Um C I, George T F and Pandey L N 1993 Phys. Rev. A 48 2716
[19] Ji J Y, Kim J K, Kim S P and Soh K S 1995 Phys. Rev. A 52 3352
[20] Song D Y 2000 Phys. Rev. A 61 024102
[21] Barton G 1986 Ann. Phys. 166 322
[22] Felder G, Frolov A, Kofman L and Linde A 2002 Phys. Rev. D 66 023507
[23] Kim S P 2006 J. Korean Phys. Soc. 49 764
[24] Miller P A and Sarkar S 1998 Phys. Rev. E 58 4217
[25] Schack R and Caves C M 1996 Phys. Rev. E 53 3387
[26] Schack R and Caves C M 1996 Phys. Rev. E 53 3257
[27] Hofmann H and Nix J R 1983 Phys. Lett. B 122 117
[28] Salbi N A, Kouri D I, Baer M and Pollak E 1985 J. Chem. Phys. 82 4500
[29] Brink D M and Smilansky V 1983 Nucl. Phys. A 405 301
[30] Cooper F, Kimball A M and Simmons L M 1985 Phys. Rev. D 32 2056
[31] Wytse van Dijk, Masafumi Toyama F, Sjirk Jan Prins and Kyle Spyksma 2014 Am. J. Phys. 82 955
[32] Pedrosa I A and Guedes I 2002 Mod. Phys. Lett. B 16 637
[33] Pedrosa I A and Guedes I 2004 Int. J. Mod. Phys. B 18 1379
[34] Pedrosa I A and Guedes I 2004 Int. J. Mod. Phys. A 19 4165
[35] Baskoutas S and Jannusis A 1992 J. Phys. A: Math. Gen. 25 L1299
[36] Baskoutas S, Jannusis A and Mignani R 1993 J. Phys. A: Math. Gen. 26 7137
[37] Baskoutas S 1996 Quantum Semiclass. Opt. 8 989
[38] Guo G J, Ren Z Z, Ju G X and Guo X Y 2011 J. Phys. A: Math. Theor. 44 185301
[39] Guo G J, Ren Z Z, Ju G X and Long C Y 2011 J. Phys. A: Math. Theor. 44 425301
[40] Guo G J, Ren Z Z, Ju G X and Guo X Y 2012 J. Phys. A: Math. Theor. 45 115301
[41] Wang Z X and Guo D R 2000 Introduction to Special Function (Peking: Peking University Press)
[42] Berry M V 1984 Proc. R. Soc. Lond. A 392 45
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