RESONANCES IN ANHARMONIC-OSCILLATORS - DETECTION AND SURPRISES

A coupled linear-nonlinear variational strategy is adopted to study re sonances in the quartic anharmonic oscillator system via the stabilisa tion method. Quite a few hitherto unexplored features show up in this case. The observed dependence of the energy of such quasi-bound states on the coupling parameter is employed to explain the unsuitability of a perturbative approach. Localised quasi-bound states are found even when there are no classical turning points. The origin of this peculia r quantum effect is traced. Finally, level-crossing problems and the a ssociated quasi-degenerate situation are also noted and analysed.