NONPERTURBATIVE EFFECTIVE POTENTIALS OF QUANTUM OSCILLATORS

Non perturbative analogues of the Gaussian effective potential (GEP) a re defined for quantum oscillators obeying q-or (qp)-deformed commutat ion relations. These are called the non perturbative q-effective poten tial (NP(q)EP) and the non perturbative qp effective potential (NP(qp) EP), in the respective cases. A system-specific effective potential (S SEP) is also introduced by means of an additional minimization with re spect to the q or q and p parameters. The method is applied to q and ( qp) oscillators of the quartic and sextic types. The SSEP in the case of ground states of the q-oscillators corresponds to q = 1, which is t he ordinary bosonic limit. A potential shape transition that involves the conversion of a double well to a single well or vice versa, is see n to exist in the case of quantum oscillators sitting in a double well potential.