A standard rule of thumb about whether a quantum Hamiltonian H = -A + V(x) has purely discrete spectrum or some continuous spectrum is the following. Look at the volume {(p, q) Ip* + V(q) <E} in R*“. If this volume is finite for all E, the standard wisdom is that H has only discrete spectrum. This standard wisdom also says that if this volume is infinite for some E < oo, then the spectrum is no...