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Journal of Radio Electronics

A model of quantum particle behavior in a potential well with a moving wall

Alexey Kartsev, A.A. Safronov, M.I. Makhov

Published Mar 1, 2024• 0 citations
Publisher

Abstract

In this paper, we find an analytical expression for the energy spectrum of a particle in a one-dimensional potential well with infinitely high walls. One of the walls with the coordinate x = 0 is motionless, the other wall, which has the coordinate x = a at the initial moment of time, moves at a constant speed. The results obtained can be used to modulate the operation of vacuum nanodevices.

DOI
10.30898/1684-1719.2024.3.1

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In this paper, we find an analytical expression for the energy spectrum of a particle in a one-dimensional potential well with infinitely high walls. One of the walls with the coordinate x = 0 is motionless, the other wall, which has the coordinate x = a at the initial moment of time, moves at a constant speed. The results obtained can be used to modulate the operation of vacuum nanodevices.
The quantum behavior of a particle in a one-dimensional infinite square well potential with a moving wall is studied. The particle is assumed to be initially prepared in the coherent state (Gaussian wave packet) and although the boundary is far from the particle, it is shown that the changing of the boundary conditions can instantaneously affect the dynamical behavior of the particle. It is also shown that the initial state can evolve into a squeezed state, and in some cases the spreading of the wavepacket could be suppressed. Finally the Pancharatnam phase is also discussed.
The expansion problem of the wavefunctions of a stationary state for a particle in one dimensional potential well with infinitely high walls in studied. We found, in the interval ( 0≤x≤a ), that the wavefunctions of a stationary state can be expressed as the superposition of two plane waves, which traveling in the opposite directions, when the energy quantum number n is even. However, it can not be done when n is odd, because they are not the period functions in this interval. If only if the width of the well tends to infinity, or n is very large, and the expanding coefficients on the base of continuous spectrum become to the superposition of two symmetrical delta functions, all of the stationary wavefunctions can be expanded as the superposition of two plane waves.