Flow dynamics of the resonances of a two-dimensional circular quantum well

Bound states and resonances are physically important solutions of the time-independent Schrödinger equation for a given quantum-mechanical potential. One can find these states using numerical analysis techniques by searching for poles of the scattering amplitude, or equivalently by locating the zeros of particular transcendental complex-valued functions. We show that the evolution of these solutions displays much deeper behavior than one may assume when parameters of the potential are varied, giving insight into the relationship between different types of solutions.