Quantum Force Induced on a Partition Wall in a Harmonic Potential

Abstract

Boundary effects in quantum mechanics are examined by considering a partition wall inserted at the centre of a harmonic oscillator system. We put an equal number of particles on both sides of the impenetrable wall keeping the system under finite temperatures. When the wall admits distinct boundary conditions on the two sides, then a net force is induced on the wall. We study the temperature behaviour of the induced force both analytically and numerically under the combination of the Dirichlet and the Neumann conditions, and determine its scaling property for two statistical cases of the particles: fermions and bosons. We find that the force has a nonvanishing limit at zero temperature T = 0 and exhibits scalings characteristic to the statistics of the particles. We also see that for higher temperatures the force decreases according to 1/sqrt{T}, in sharp contrast to the case of the infinite potential well where it diverges according to sqrt{T}. The results suggest that, if such a nontrivial partition wall can be realized, it may be used as a probe to examine the profile of the potentials and the statistics of the particles involved.