  Recently developed strong-coupling theory open up the possibility of treating
quantum-mechanical systems with hard-wall potentials via perturbation theory.
To test the power of this theory we study here the exactly solvable quantum
mechanics of a point particle in a one-dimensional box. Introducing an
auxiliary harmonic mass term $m$, the ground-state energy $E^{(0)$ can be
expanded perturbatively in powers of $1/md$, where $d$ is the box size. The
removal of the infrared cutoff $m$ requires the resummation of the series at
infinitely strong coupling. We show that strong-coupling theory yields a
fast-convergent sequence of approximations to the well-known quantum-mechanical
energy $E^{(0)= \pi ^2/2d^2$.
