Quantized vortices around wavefunction nodes. II

Quantized vortices can occur around nodes of wavefunctions. This fact, discovered by Dirac (1931) but little noted since, is rederived here and examples are discussed. The derivation depends only on the wavefunction being single valued and continuous. Since the derivation does not depend upon the dynamical equations, the quantized vortices are expected to occur for many types of waves (i.e., electromagnetic, acoustic, etc.). Such vortices have appeared in the calculations (McCullough and Wyatt, Kuppermann) of the H + H2 molecular collisions and play a role in the chemical kinetics. In a companion paper, it is shown that quantized vortices occur when optical waves are internally reflected from the face of a prism or particle beams are reflected from potential energy barriers.