Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure

Jie Quanlin; Wang Shunjin; Wei Lianfu

Chinese Physics C> 1998, Vol. 22> Issue(2) : 111-116

Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure

Institute of Modern Physics Southwest Jiaotong University,Chengdu 610031

Abstract
HTML
Reference
Related

PDF

Abstract：
For quantum systems with semi-simple Lie algebraic structures,the exact solutions of the equations of motion are obtained by means of algebraic dynamics.The Hamiltonian is transformed into a linear function of Cartan operators by a set of gauge transformations. The coefficients of the gauge transformations are determined by a set of ordinary differential equations.From the inverses of these gauge transformations,the solutions of the Schrodinger equation,as well as a set of dynamic constants of motion (dynamic invariant operators) are obtained. An SU(3) model serves as an example.

References

[1]

Wang S J, Li F L, Weiguny A. Phys. Lett, 1993,A180 (1):189-196[2] Paul W. Rev. Mod. Phys., 1990,62 (3):531-540[3] Brown L S. Phys. Rev. Lett, 1991, 66 (5):527-529[4] Wang S J, Zuo W, Weiguny A et al. Phys. Lett, 1994, A196 (1):7-12; Wang S J, Zuo W. Phys. Lett, 1994, A196 (1):13-19; Zuo W, Wang S J. Acta Physica Sinica, 1995, 44 (9):1353-1362,1363-1372[5] Shore B W, Knihgt P L. J. Mod. Optics, 1993, 40 (7): 1195-1238[6] Yu S, Rauch H, Zhang Y. Phys. Rev., 1995, A52 (4):2585-2590[7] Kibler M, Negadi T. Lett. Nuovo Cimento, 1980, 37 (1):225-229[8] Cornish F H. J. Phys., 1984, A17 (2):323-334.[9] Chen A C, Kibler M. Phys. Rev., 1985, A31 (7):3960-3969[10] Xu B W, Zeng Q. Acta Physica Sinica, 1991, 40 (8):1212-1216[11] Xu B W, Gu W H. Acta Physica Sinica, 1993, 42 (7):1050-1056[12] Wei J, Norman E. J. Math. Phys., 1963, 4 (1):575-582[13] Shi S, Rabitz H. J. Chem. Phys., 1988, 88 (12):7508-7521[14] Gilmore R, Yuan J M. J. Chem. Phys., 1987,86 (1):130-139; 1989,91(2):917-923[15] Recamier J, Micha D A, Gazdy B. Chem. Phys. Lett., 1985, 119(5): 383-387; J. Chem. Phys., 1986,85 (9):5093-5 100[16] Benjamin I. J. Chem. Phys., 1986, 85(10):5611-5624[17] Gilmore R Lie Group, Lie Algebra and Some of Their Applications. New York: Wiley, 1974; Cheng J Q. Group Representation Theory for Physicists. Singapore: World Scientific, 1989[18] Lewis H R J. Math. Phys., 1969, 10 (8):1458-1473[19] Wan Zhexian. Lie Algebra(in Chinese). Beijin: Scientific Press, 1964(万哲先. 李代数. 北京:科学出版社. 1964)[20] Singh S. Phys. Rev., 1982, A25(7):3206-3211[21] Bonatsos D, Daskaloyannis C, Lalazissis G A. Phys. Rev., 1993, A47 (7):3448--3452[22] Khidekel V. Phys. Rev., 1995, E52 (3):2510-2521

[1]	WANG Peng , WANG Shun-Jin . Analytic Exact Solution of One-Dimentional Nonautonomous Classical Harmonic Oscillator. Chinese Physics C, 2005, 29(7): 651-656.
[2]	SHI Guo-Fang , DENG Hui , XIONG Hua-Hui , SHI Kang-Jie . Quantum States and Soltion Solutions on Noncommutative Orbifold R4/G. Chinese Physics C, 2004, 28(10): 1033-1039.
[3]	LIU Wang-Yun , YANG Zhan-Ying , ZHAO Liu . Generalized Toda Mechanics Associated with Classical Lie Algebras D_r. Chinese Physics C, 2004, 28(4): 359-364.
[4]	WANG Shun-Jin , GUO Yuan-Jun . Complementary Chaos and Spin Polarization Stability in Cyclotrons Studied from the Nonautonomous SU(2)Dynamical System. Chinese Physics C, 2003, 27(12): 1123-1127.
[5]	ZHAO Wei-Qin , JV Chang-Sheng . Analytic Solution of Ground State for Coulomb Plus Linear Potential. Chinese Physics C, 2002, 26(4): 299-304.
[6]	LIU Fang , LI Jun-Qing , XING Yong-Zhong . Quantum Classical Correspondence in a 2-Dimensional Deformed Harmonic Oscillator System. Chinese Physics C, 2002, 26(9): 949-954.
[7]	YANG ZhanYing , ZHAO Liu , ZHEN Yi . Exact Solution of Super Liouville Model. Chinese Physics C, 2000, 24(2): 91-97.
[8]	Ma Tao , Ni Zhixiang . Non-Harmonic Oscillator and New Conditionally Exactly Solvable Potentials. Chinese Physics C, 1999, 23(7): 650-654.
[9]	Chen Changyuan , Liu Youwen . Exact Solutions of Non-spherical Harmonic Oscillator Potential. Chinese Physics C, 1999, 23(9): 865-872.
[10]	Xie Mi , Jin Baiqi , Ma Zhongqi . L^± Operators and Quantum Enveloping Algebras. Chinese Physics C, 1996, 20(7): 617-624.
[11]	Hu Zhanning . Three-Dimensional Exactly Solvable Model With Cubic Lattice. Chinese Physics C, 1994, 18(9): 813-820.
[12]	HU Zhan-Ning . Central Extension of the Quantum Deformed Virasoro Algebra. Chinese Physics C, 1991, 15(10): 898-905.
[13]	FU Hong-Chen . INHOMOGENEOUS DIFFERENTIAL REALIZATION,BOSON-FERMION REALIZATION OF LIE SUPERALGEBRA B(0,1) AND ITS REPRESENTATIONS. Chinese Physics C, 1990, 14(2): 126-135.
[14]	SUN Chang-Pu . ON BOSON REALIZATIONS AND INHOMOGENEOUS DIFFERENTIAL REALIZATION FOR LIE ALGEBRAS AND THEIR REPRESENTATIONS. Chinese Physics C, 1990, 14(9): 788-795.
[15]	YAN Jun-Hu . EXACT SOLUTION OF THE PAULI EQUATION IN THE FIELD OF A 'T HOOFT-POLYAKOV MONOPOLE. Chinese Physics C, 1985, 9(3): 367-370.
[16]	WU Ji-Min , LU Jing-Xian , ZHAO Pei-Ying . AN ANALYTIC EXPRESSION FOR NON-SINGLET COMPONENT OF NUCLEON STRUCTURE FUNCTIONS TO THE NEXT ORDER EFFECTS. Chinese Physics C, 1984, 8(1): 10-16.
[17]	WANG Wei-Wei , ZHANG Yu-Shun , LI YANG , RUAN Tu-Nan . UNITARY THEORY OF BARYON-SYSTEM. Chinese Physics C, 1983, 7(1): 57-66.
[18]	ZHANG YU-SHUN , LI YANG-GUO , WANG WEI-WEI , CHEN XIAO-TIAN , RUAN TU-NAN . THE SU(6) “UNITARY ENERGY BAND” STRUCTURE IN THE TRIBARYON SYSTEM. Chinese Physics C, 1981, 5(5): 521-530.
[19]	WANG WEI-WEI , ZHANG YU-SHUN , LI YANG-GUO , CHEN XIAO-TIAN , RUAN TU-NAN . THE “UNIRARY ENERGY BAND” STRUCTURE IN THE BARYON-ANTIBARYON SYSTEN. Chinese Physics C, 1981, 5(4): 441-451.
[20]	HSXJ KUNG-NGOU . MASTER EQUATION FOR QUANTUM SYSTEMS. Chinese Physics C, 1978, 2(4): 359-367.

Access

Get Citation

Jie Quanlin, Wang Shunjin and Wei Lianfu. Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure[J]. Chinese Physics C, 1998, 22(2): 111-116.

Jie Quanlin, Wang Shunjin and Wei Lianfu. Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure[J]. Chinese Physics C, 1998, 22(2): 111-116. shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 1900-01-01
Revised: 1900-01-01

Article Metric

Article Views(3151)
PDF Downloads(583)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure

Corresponding author: Jie Quanlin,

Institute of Modern Physics Southwest Jiaotong University,Chengdu 610031

Received Date: 1900-01-01

Accepted Date: 1900-01-01

Available Online: 1998-02-05

Abstract: For quantum systems with semi-simple Lie algebraic structures,the exact solutions of the equations of motion are obtained by means of algebraic dynamics.The Hamiltonian is transformed into a linear function of Cartan operators by a set of gauge transformations. The coefficients of the gauge transformations are determined by a set of ordinary differential equations.From the inverses of these gauge transformations,the solutions of the Schrodinger equation,as well as a set of dynamic constants of motion (dynamic invariant operators) are obtained. An SU(3) model serves as an example.

HTML

Reference (1)

Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article