  Convergent semiclassical trace formulae for the density of states and
cohesive force of a narrow constriction in an electron gas, whose classical
motion is either chaotic or integrable, are derived. It is shown that mode
quantization in a metallic point contact or nanowire leads to universal
oscillations in its cohesive force: the amplitude of the oscillations depends
only on a dimensionless quantum parameter describing the crossover from chaotic
to integrable motion, and is of order 1 nano-Newton, in agreement with recent
experiments. Interestingly, quantum tunneling is shown to be described
quantitatively in terms of the instability of the classical periodic orbits.
