  The so-called "Quantum Inequalities", and the "Quantum Interest Conjecture",
use quantum field theory to impose significant restrictions on the temporal
distribution of the energy density measured by a time-like observer,
potentially preventing the existence of exotic phenomena such as "Alcubierre
warp-drives" or "traversable wormholes". Both the quantum inequalities and the
quantum interest conjecture can be reduced to statements concerning the
existence or non-existence of bound states for a certain one-dimensional
quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a
simple proof of one version of the Quantum Interest Conjecture in (3+1)
dimensional Minkowski space.
