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Journal of Beijing Union University

A Study on Quantum Spectrums and Closed-orbit in the System of One-dimensional Nano-microstructure

Jun Lu

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

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.

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Acta Physica Sinica•Jan 1, 2004•8 citations
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.
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.
The quantum spectrum function is introduced by means of the eigenvalues and the eigenfunctions in the system of varying 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. The researches about these systems are very important in the field of applied science, for example, quantum computer, quantum calculation, and quantum information.