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Journal of Guangxi Normal University

Transition Process for Nano-microstructure

Li Fei

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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 containing a lot of information about the classical orbits of a particle from one point to another.These results provide evidence for the classical-quantum correspondence in the system of nano-microstructure.

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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 containing a lot of information about the classical orbits of a particle from one point to another.These results provide evidence for the classical-quantum correspondence in the system of 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.
Closed-orbit theory is extended to interpret a kind of new classical-quantum correspondence principle, in term of eigenvalues and the eigenfunctions. The relation of the classical orbit and the quantum mechanics of dynamical behavior is examined in the system of one-dimensional nano-microstructure. The research proposed that the Fourier transformation of the quantum spectrum function contains a lot of information about the classical orbits of a particle from one point to another. In this paper, we describe the physical ideas under-lying the closed-orbit theory, and we present our calculations based upon the theory.
A new quantum spectrum function is defined using the energy eigenvalues and eigenfunctions of a one-dimensional nana-microstructure system.As an example of the calculation of quantum spectrum function,the one-dimensional closed orbits motion of a billiard was considered.It is found that the Fourier transform of the quantum spectrum function corresponds with the classical closed-orbits in the system.These results give new evidence about the classical-quantum correspondence in the system of one-dimensional nana-microstructure.
Two-dimensional nanomaterials are becoming the focus of intensive research due to their novel physical properties and the potential applications in nanodevices. We define a quantum spectrum function using the eigenvalues and the eigenfunctions in the system of two-dimensional nanomaterials. We find that the Fourier transform of the quantum spectrum function reveals a lot of information of the classical orbits from one point to another for a particle in the two-dimensional nanomaterials. 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 one-dimensional and three-dimensional systems. The researches about these systems are very important in the field of applied science.