Generalized Coherent States of a Particle in a Time-Dependent Linear Potential
L. Krache1, M. Maamache1, Y. Saadi1, A. Beniaiche2
1Lab PQSD, Faculté des Sciences, Université Ferhat Abbas de Sétif, Sétif 19000, Algeria2Lab SPONL, Faculté des Sciences de l'Ingénieur, Université Ferhat Abbas de Sétif, Sétif 19000, Algeria
Generalized Coherent States of a Particle in a Time-Dependent Linear Potential
L. Krache1, M. Maamache1, Y. Saadi1, A. Beniaiche2
1Lab PQSD, Faculté des Sciences, Université Ferhat Abbas de Sétif, Sétif 19000, Algeria2Lab SPONL, Faculté des Sciences de l'Ingénieur, Université Ferhat Abbas de Sétif, Sétif 19000, Algeria
摘要 We derive, with an invariant operator method and unitary transformation approach, that the Schrödinger equation with a time-dependent linear potential possesses an infinite string of shape-preseving wave-packet states |φα,λ>(t)> having classical motion. The qualitative properties of the invariant eigenvalue spectrum (discrete or continuous) are described separately for the different values of the frequency ω of a harmonic oscillator. It is also shown that, for a discrete eigenvalue spectrum, the states |φα,n>(t)> could be obtained from the coherent state |φα,0>(t).
Abstract： We derive, with an invariant operator method and unitary transformation approach, that the Schrödinger equation with a time-dependent linear potential possesses an infinite string of shape-preseving wave-packet states |φα,λ>(t)> having classical motion. The qualitative properties of the invariant eigenvalue spectrum (discrete or continuous) are described separately for the different values of the frequency ω of a harmonic oscillator. It is also shown that, for a discrete eigenvalue spectrum, the states |φα,n>(t)> could be obtained from the coherent state |φα,0>(t).
L. Krache;M. Maamache;Y. Saadi;A. Beniaiche. Generalized Coherent States of a Particle in a Time-Dependent Linear Potential[J]. 中国物理快报, 2009, 26(7): 70307-070307.
L. Krache, M. Maamache, Y. Saadi, A. Beniaiche. Generalized Coherent States of a Particle in a Time-Dependent Linear Potential. Chin. Phys. Lett., 2009, 26(7): 70307-070307.
[1] Rau A and Unnikrishnan K 1999 Phys. Lett. A 222 304 [2] Guedes I 2001 Phys. Rev. A 63 034102 [3] Feng M 2001 Phys. Rev. A 64 034101 [4] Bauer J 2002 Phys. Rev. A 65 036101 [5] Bekkar H et al 2003 Phys. Rev. A 68 016101 [6] Luan P G and Tang C S 2005 Phys. Rev. A 71014101 [7] Dunkel J and Trigger S A 2005 Phys. Rev. A 71052102 [8] Bowman G E 2006 J. Phys. A 39 157 [9] Kim S P 2006 J. Korean Phys. Soc. 44 464 [10] Lu G B et al 2006 Phys. Lett. A 357 181 [11] Lewis H R Jr et al 1969 J. Math. Phys. 101458 [12] Schrodinger E 1926 Naturwiss 14 664 [13] Glauber R J 1963 Phys. Rev. 130 2529 [14] Klauder J R 1960 Ann. Phys. (N. Y.) 11 123 Klauder J R 1963 J. Math. Phys. 4 1055 Klauder J R 1963 J. Math. Phys. 4 1058 [15] Sudarshan E C G 1963 Phys. Rev. Lett. 10 227 [16] Klauder J R and Sudarshan E C G 1968 Fundamentals ofQuantum Optics (New York: Benjamin) [17] Senitzky R 1954 Phys. Rev. 95 1115 [18] Plebanski J 1956 Phys. Rev. 101 1825 Plebanski J 1954 Bull. Acad. Polon. 11 213 Plebanski J 1955 Bull. Acad. Polon. 14 275 [19] Husimi K 1953 Prog. Theor. Phys. 9 381 [20] Epstein S T 1959 Am. J. Phys. 27 291 [21] Nieto M M 1997 Phys. Lett. A 229 135 [22] Roy S M and Singh V 1982 Phys. Rev. D 25 3413 [23] Satyanarayana M V 1985 Phys. Rev. D 32 3400 [24] Maamache M and Saadi Y 2008 arXiv:0804 4289v1 [25] Barton G 1986 Ann. Phys. (N. Y.) 166 322 [26] Pedrosa I A et al 2004 Int. J. Mod. Phys. B 18 1379 [27] Abramowitz M and Stegun I A 1970 HandbookMathematical Functions (New York: Dover) sec 19
2009, Vol. 26 
