Non perturbative effective potentials of quantum oscillators

Non perturbative analogues of the Gaussian effective potential (GEP) are defined for quantum oscillators obeying q-or (q,p)-deformed commutation relations. These are called the non perturbative q-effective potential (NPqEP) and the non- perturbative qp effective potential (NPsub(qp)EP), in the respective cases. A system-specific effective potential (SSEP) is also introduced by means of an additional minimization with respect to the q or q and p parameters. The method is applied to q and (q,p) 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 the ordinary bosonic limit. A potential shape transition that involves the conversion of a double well to a single well or vice versa, is seen to exist in the case of quantum oscillators sitting in a double well potential. (author). 13 refs., 2 figs