  The eigenvalue density of a quantum-mechanical system exhibits oscillations,
determined by the closed orbits of the corresponding classical system; this
relationship is simple and strong for waves in billiards or on manifolds, but
becomes slightly muddy for a Schrodinger equation with a potential, where the
orbits depend on the energy. We discuss several variants of a way to restore
the simplicity by rescaling the coupling constant or the size of the orbit or
both. In each case the relation between the oscillation frequency and the
period of the orbit is inspected critically; in many cases it is observed that
a characteristic length of the orbit is a better indicator. When these matters
are properly understood, the periodic-orbit theory for generic quantum systems
recovers the clarity and simplicity that it always had for the wave equation in
a cavity. Finally, we comment on the alleged "paradox" that semiclassical
periodic-orbit theory is more effective in calculating low energy levels than
high ones.
