  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.
