Quantum Spectra and Classical Orbits in Nano-Microstructure


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A kind of new classical-quantum correspondence principle is proposed using the idea of closed-orbit theory. The quantum spectrum function is introduced by means of the eigenvalues and the eigenfunctions in the system of one-dimensional nano-microstructure. The Fourier transformation of the quantum spectrum function is found corresponding with the classical orbits in the system. These results give new evidence about the classical-quantum correspondence. All the methods and results can be used in a lot of other systems, including some two-dimensional and three-dimensional systems. The researches about these systems are very important in the field of applied science, for example, molecular reaction dynamics and quantum information.



Advanced Materials Research (Volumes 160-162)

Edited by:

Guojun Zhang and Jessica Xu




J. Lu and X. M. Wang, "Quantum Spectra and Classical Orbits in Nano-Microstructure", Advanced Materials Research, Vols. 160-162, pp. 625-629, 2011

Online since:

November 2010





[1] M.C. Gutzwiller: J. Math. Phys. Vol. 12 (1971), p.343.

[2] M.C. Gutzwiller: Chaos in Classical and Quantum Mechanics (Springer-Verlag, New York 1990).

[3] D. Kleppner and J.B. Delos: Found. Phys. Vol. 31 (2001), p.593.

[4] M.L. Du and J.B. Delos: Phys. Rev. Lett. Vol. 58 (1987), p.1731.

[5] M.L. Du and J.B. Delos: Phys. Rev. A Vol. 38 (1988), p.1896.

[6] M.L. Du and J.B. Delos: Phys. Rev. A Vol. 38 (1988), p. (1913).

[7] D.A. Sadovskii, J.A. Shaw and J.B. Delos: Phys. Rev. Lett. Vol. 75 (1995), p.2120.

[8] P.A. Dando, T.S. Monteiro and S.M. Owen: Phys. Rev. Lett. Vol. 75 (1998), p.2797.

[9] A. Matzkin, P.A. Dando and T.S. Monteiro: Phys. Rev. A Vol. 66 (2002), p.013410.

[10] M.R. Haggerty and J.B. Delos: Phys. Rev. A Vol. 61 (2000), p.053406.

[11] J. Main and V.A. Mandelshtam and H.S. Taylor: Phys. Rev. Lett. Vol. 79 (1997), p.825.

[12] R.W. Robinett: J. Math. Phys. Vol. 39 (1998), p.278.

[13] R.W. Robinett: Am. J. Phys. Vol. 67 (1999), p.67.

[14] J.U. Nöckel, and A.D. Stone: Nature Vol. 385 (1997), p.45.

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