  A number of derivations of the standard neutrino oscillation formula are
known, each one providing its own unique insights. Common to all treatments is
the assumption that neutrinos propagate freely between source and detector, as
indeed they do in all experiments thus far conducted. Here we consider how
neutrinos oscillate when, contrary to the usual set-up, they are bound in a
potential well. The focus in particular is on nonrelativistic neutrinos with
quasi-degenerate masses, for which oscillations in free space are described by
the same formula, to lowest order, as relativistic neutrinos. Trapping these
particles engenders corrections to their oscillation frequencies because the
interference terms are between discrete energy levels rather than continuous
spectra. Especially novel is the frequency shift that occurs due to the
dependence of the energy levels on the mass of the neutrino: this part of the
correction is nonvanishing even in the extremely nonrelativistic limit,
reflecting the fact that the neutrino mass states have different zero-point
energies in the well. Building an apparatus that can trap neutrinos is a
futuristic prospect to say the least, but these calculations nonetheless shine
a light on certain basic aspects of the flavor-oscillation phenomenon.
