  We show that the rational Calogero model with suitable boundary condition
admits quantum states with non-equispaced energy levels. Such a spectrum
generically consists of infinitely many positive energy states and a single
negative energy state. The new states appear for arbitrary number of particles
and for specific ranges of the coupling constant. These states owe their
existence to the self-adjoint extensions of the corresponding Hamiltonian,
which are labelled by a real parameter z. Each value of z corresponds to a
particular spectrum, leading to inequivalent quantizations of the model.
