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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Shape and Fourier's spectra of a quantum packet in a box for electron motion with specified initial velocities

Andrey L. Sanin, Andrey T. Bagmanov

Published Apr 29, 2005• 0 citations
Publisher

Abstract

Oscillatory motion of quantum packet at the specific initial and zeroth boundary conditions with arbitrary initial velocity is investigated analytically and numerically. Influence of integer and half-integer initial velocities on the spatially temporal properties of solutions has been studied in detail. Hydrodynamical variables such as the probability density, mean values of coordinate and current, phase trajectories for coordinate and current, and Fourier spectra of these quantities were calculated. The behavior of quantum potential and kinetic energy near the nodal point was also analyzed.

DOI
10.1117/12.619489

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Oscillatory motion of quantum packet at the specific initial and zeroth boundary conditions with arbitrary initial velocity is investigated analytically and numerically. Influence of integer and half-integer initial velocities on the spatially temporal properties of solutions has been studied in detail. Hydrodynamical variables such as the probability density, mean values of coordinate and current, phase trajectories for coordinate and current, and Fourier spectra of these quantities were calculated. The behavior of quantum potential and kinetic energy near the nodal point was also analyzed.
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The quantum dynamics of a hydrogen-like atom confined in one-dimensional box with oscillating walls is studied.The description of the system is reduced to a one-dimensional Schrödinger equation for Coulomb potential with time-dependent boundary conditions, which is solved numerically.Using the obtained solution, the average kinetic energy and binding energies are calculated as a function of time.It is found that both the average kinetic energy and the binding energies are periodic in time with the period depending on the wall's oscillation parameters.The probability density is also analyzed as a function of time and coordinate.