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In this paper, we handle the Hamiltonian of the particles that are affected by the linear-damping and time-dependent external force given by two different canonical transformations by using the theory of generalized quantum linear transformation. We give the rigorous solution of evolution operator, and the expectation values of coordinate and momentum of the particles quantum fluctuations. Results show that 1) the two regular translations are equivalent; 2) linear damping has a squeezing effect on the momentum of particle, and the deviation of the momentum attenuates with time t according to the rule of negative exponent, and the bigger the damping coefficient, the faster the attenuation is; 3) the expectation values of coordinate and momentum of the particle are equal to their classical values correspondingly.
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Keywords:
- linear-damping /
- time-dependent external force /
- particles /
- evolution operator
[1] Nassar A B 2002 J. Opt. B 4 226
[2] Brown L S, Lee C 1978 Phys. Rev. D 18 2180
[3] Lo C F 1991 Phys. Rev. A 43 404
[4] Nassar A B 1986 Phys. Rev. A 32 1862
[5] Ikot A N, Ituen E E, Essien I E, Akpabio L 2008 Turk J. Phys. 32 305
[6] Yasuda M, Shimizu F 1996 Phys. Rev. Lett. 77 3090
[7] Hinds E A, Boshier M G, Hughes I G 1998 Phys. Rev. Lett. 80 645
[8] Brown L S 1991 Phys. Rev. Lett. 66 527
[9] Feng M, Wang K 1995 Phys. Lett. A 197 135
[10] Lewis Jr H R 1968 J. Math. Phys. 9 1976
[11] Lewis Jr H R, Riesenfield W B 1969 J. Math. Phys. 10 1458
[12] Li L, Li B Z, Liang J Q 2001 Acta Phys. Sin. 50 2077 (in Chinese) [李玲, 李伯臧, 梁九卿 2001 50 2077]
[13] Khandekar D C, Lauwande S V 1975 J. Math. Phys. 16 384
[14] James W, Edward N 1963 J. Math. Phys. 4 4
[15] Wang P, Yang X E, Song X H 2003 Acta Phys. Sin. 52 2957 (in Chinese) [王平, 杨新娥, 宋小会 2003 52 2957]
[16] Feng M 2001 Phys. Rev. A 64 034101
[17] Zhang Y D, Tang Z 1994 Nuovo Cimento B 109 387
[18] Yu S X, Zhang Y D 1995 Commun. Theor. Phys. 24 185
[19] Xu X W, Zhang Y D 1997 Chin. Phys. Lett. 14 812
[20] Xu X W 2000 J. Phys. A 33 2447
[21] Xu X W, Ren T Q, Liu S Y, Dong Y M, Zhao J D 2006 Acta Phys. Sin. 55 535 (in Chinese) [徐秀玮, 任廷琦, 刘姝延, 董永绵, 赵继德 2006 55 535]
[22] Wang X Q, Zhou L Y, Lu H X 2008 Acta Phys. Sin. 57 6736 (in Chinese) [王晓芹, 周立友, 逯怀新 2008 57 6736]
[23] Xu X W, Ren T Q, Chi Y J, Zhu Y L, Liu S Y 2006 Acta Phys. Sin. 55 3892 (in Chinese) [徐秀玮, 任廷琦, 迟永江, 朱友良, 刘姝延 2006 55 3892]
[24] Nassar A B 1986 J. Math. Phys. 27 755
[25] Malkin I A, Man'ko V I 1970 Phys. Lett. A 71 317
[26] Peng H W 1980 Acta Phys. Sin. 29 1084 (in Chinese) [彭恒武 1980 29 1084]
[27] Ikot A N, Uwah E J, Akpabio L E, Akpan I O 2010 J. Phys. Educ. 4 331
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[1] Nassar A B 2002 J. Opt. B 4 226
[2] Brown L S, Lee C 1978 Phys. Rev. D 18 2180
[3] Lo C F 1991 Phys. Rev. A 43 404
[4] Nassar A B 1986 Phys. Rev. A 32 1862
[5] Ikot A N, Ituen E E, Essien I E, Akpabio L 2008 Turk J. Phys. 32 305
[6] Yasuda M, Shimizu F 1996 Phys. Rev. Lett. 77 3090
[7] Hinds E A, Boshier M G, Hughes I G 1998 Phys. Rev. Lett. 80 645
[8] Brown L S 1991 Phys. Rev. Lett. 66 527
[9] Feng M, Wang K 1995 Phys. Lett. A 197 135
[10] Lewis Jr H R 1968 J. Math. Phys. 9 1976
[11] Lewis Jr H R, Riesenfield W B 1969 J. Math. Phys. 10 1458
[12] Li L, Li B Z, Liang J Q 2001 Acta Phys. Sin. 50 2077 (in Chinese) [李玲, 李伯臧, 梁九卿 2001 50 2077]
[13] Khandekar D C, Lauwande S V 1975 J. Math. Phys. 16 384
[14] James W, Edward N 1963 J. Math. Phys. 4 4
[15] Wang P, Yang X E, Song X H 2003 Acta Phys. Sin. 52 2957 (in Chinese) [王平, 杨新娥, 宋小会 2003 52 2957]
[16] Feng M 2001 Phys. Rev. A 64 034101
[17] Zhang Y D, Tang Z 1994 Nuovo Cimento B 109 387
[18] Yu S X, Zhang Y D 1995 Commun. Theor. Phys. 24 185
[19] Xu X W, Zhang Y D 1997 Chin. Phys. Lett. 14 812
[20] Xu X W 2000 J. Phys. A 33 2447
[21] Xu X W, Ren T Q, Liu S Y, Dong Y M, Zhao J D 2006 Acta Phys. Sin. 55 535 (in Chinese) [徐秀玮, 任廷琦, 刘姝延, 董永绵, 赵继德 2006 55 535]
[22] Wang X Q, Zhou L Y, Lu H X 2008 Acta Phys. Sin. 57 6736 (in Chinese) [王晓芹, 周立友, 逯怀新 2008 57 6736]
[23] Xu X W, Ren T Q, Chi Y J, Zhu Y L, Liu S Y 2006 Acta Phys. Sin. 55 3892 (in Chinese) [徐秀玮, 任廷琦, 迟永江, 朱友良, 刘姝延 2006 55 3892]
[24] Nassar A B 1986 J. Math. Phys. 27 755
[25] Malkin I A, Man'ko V I 1970 Phys. Lett. A 71 317
[26] Peng H W 1980 Acta Phys. Sin. 29 1084 (in Chinese) [彭恒武 1980 29 1084]
[27] Ikot A N, Uwah E J, Akpabio L E, Akpan I O 2010 J. Phys. Educ. 4 331
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