Vortex Lattices in Quantum Mechanics

Vortex lattices are constructed in terms of linear combinations of solutions for Scr\"{o}dinger equation with a constant potential. The vortex lattices are mapped on the spaces with two-dimensional rotationally symmetric potentials by using conformal mappings and the differences of the mapped vortex-patterns are examined. The existence of vortex dipole and quadrupole is also pointed out.