  The Landau problem for inhomogeneous magnetic fields is examined in a very
general context and several interesting analogies with the Nielsen-Olesen
vortices are established. Firstly we show that the Landau problem with
non-homogeneous magnetic fields exhibits Meissner effect that is unstable
unless two-body interactions are added and vortices emerge. Using the scaling
freedom we can write the Schr\"odinger equation in terms of the scales ratio
$\kappa ={ E}/{ m }\propto 1- T/T_c $ where the last identification is realised
simply by using the Gizburg-Landau theory. We find our equations are valid in
the superconducting regime, and it is not possible for the Cooper pairs
amplitude to reach to a constant, non-zero value, and therefore the theory is
unstable. The supersymmetric quantum mechanics version, by completeness, is
also considered.
