Abstract
Using the trial-function method, the general solution of the Schrödinger equation for the time-dependent linear potential is obtained. Based on the Heisenberg correspondence principle, the solution of the classical equation of motion is derived from the quantum matrix elements.
Similar content being viewed by others
References
W.R. Greenberg, A. Klein, and C.T. Li: Phys. Rev. Lett.75 (1995) 1244.
J.J. Morehead: Phys. Rev. A53 (1996) 1285.
M.L. Liang and H.B. Wu: Phys. Scripta68 (2003) 41.
I. Guedes: Phys. Rev. A63 (2001) 034102.
M. Feng: Phys. Rev. A64 (2001) 034101.
J. Bauer: Phys. Rev. A65 (2002) 036101.
K. Husimi: Prog. Theor. Phys.9 (1953) 381.
F. Schweiter, B. Tilch, and W. Ebeling: Eur. Phys. J. B14 (2000) 157.
R. Mamkin, A. Ainsaar, and E. Reiter: Phys. Rev. E61 (2000) 6359.
G. Casati, B.V. Chirikov, D.L. Shepelyansky, and I. Guarneri: Phys. Rep.154 (1987) 77.
S. Cocke and L.E. Reichl: Phys. Rev. A53 (1996) 1746.
M.S. Chung, N.M. Miskovski, P.H. Cutler, and N. Kumar: Appl. Phys. Lett.76 (2000) 1143.
J. Fortagh, H. Ott, A. Grossmann, and C. Zimmermann: Appl. Phys. B70 (2001) 701.
H.R. Lewis: Phys. Rev. Lett.18 (1967) 510.
H.R. Lewis and W.B. Riesenfeld: J. Math. Phys.10 (1969) 1458.
Author information
Authors and Affiliations
Additional information
This project was supported by the LiuHui Fund for Applied Mathematics.
Rights and permissions
About this article
Cite this article
Liang, ML., Zhang, ZG. & Zhong, KS. Quantum—classical correspondence of the time-dependent linear potential. Czech J Phys 54, 397–402 (2004). https://doi.org/10.1023/B:CJOP.0000020579.42018.d9
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1023/B:CJOP.0000020579.42018.d9