  We consider changes of the topological charge of vortices in quantum
mechanics by investigating analytical examples where the creation or
annihilation of vortices occurs. In classical hydrodynamics of non-viscous
fluids the Helmholtz-Kelvin theorem ensures that the velocity field circulation
is conserved. We discuss applicability of the theorem in the hydrodynamical
formulation of quantum mechanics showing that the assumptions of the theorem
may be broken in quantum evolution of the wavefunction leading to a change of
the topological charge.
