“Hermite” states in the quantum interaction of vortices

Quantum effects in the dynamics of a pair of monopolar vortices, arbitrary in their nature, are described in both the Heisenberg and Schrödinger languages. This system proves to be very closely and universally related to a linear quantum oscillator, which allows us to call it a 'Hermite' system, in regard to the eigenfunctions of such an oscillator.