BENDER-WU BRANCH-POINTS IN THE CUBIC OSCILLATOR

The analytic continuation of the resonances of the cubic anharmonic oscillator to complex values of the coupling constant is studied with semiclassical and numerical methods. Bender-Wu branch points, at which level crossing occurs, are calculated and labelled by a process of analytic continuation. The different resonances are the values that a single analytic function takes on different sheets of a Riemann surface whose topology is described.