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Journal of Mathematical Physics

Quantum particle in a box with moving walls

V. V. Dodonov, A. B. Klimov, Dmitri E. Nikonov

Published Aug 1, 1993• 69 citations
Publisher

Abstract

The analytical expressions for the energy gain and transition probabilities between energy levels of a nonrelativistic quantum particle confined in a box with uniformly moving walls, including the cases of adiabatic motion and a sudden change of the size of the box was obtained.
DOI
10.1063/1.530083

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The transition probabilities of a quantum system introduced between parallel conducting walls approaching or receding from each other with arbitrary constant relative speed are evaluated in the dipole approximation. The interaction with the vacuum fluctuations of the quantum electromagnetic field inside the box induces modifications in the spontaneous emission probabilities. While the transition probabilities in free space are recovered in the ultrarelativistic limit, an enhancement or inhibition of the spontaneous emission in the nonrelativistic limit is expected according to the dipole moment orientation of the detector. These results are discussed in the context of photon generation by the moving walls. \textcopyright{} 1996 The American Physical Society.
Static potential boxes represent an area that is limited by an infinite potential wall, where there is no external potential in it. The solution of the Schrodinger equation gives a wave function that can explain the energy level and determine the probability of finding a particle at any point. The main focus of the research in this paperwas to solve the solution to the energy levels, probabilities, and expectation values of a particle in a three-dimensional box, where control limits are given for the potential box width, namely and L for each situation. In this research, the results showed that probability meetings depend on changes in box width and quantum number of particles, while particle energy levels depend on the length of the box and the quantum number of particles. Based on the relation between probabilities and expectation values, the most stable size of the box to find the particles in ground state to the fourth excitation state is at the width of and L .
The temporal energy spectrum Es,a(t) and the uncertainty product Delta psa(t) Delta x,s,a(t) are derived from an analytical solution psi (x,t) of the initial-boundary-value problem for the Schrodinger equation of a particle contained between moving potential walls at x=+or-s(t), which are set in motion according to an arbitrary (non-relativistic) translation s=s(t) at time t=0. Both symmetrical (s) and antisymmetrical (a) particle states are considered as initial conditions in the region -s(0)<or=x<or=+s(0). The physical implications of the compression and expansion of the probability density by the moving walls on the wave mechanics of the particle are discussed. The results are understandable within the statistical interpretation of quantum theory.