  The quantum dynamics of a two-dimensional charged spin $1/2$ particle is
studied for general, symmetry--free curved surfaces and general, nonuniform
magnetic fields that are, when different from zero, orthogonal to the defining
two surface. Although higher Landau levels generally lose their degeneracy
under such general conditions, the lowest Landau level, the ground state,
remains degenerate. Previous discussions of this problem have had less
generality and/or used supersymmetry, or else have appealed to very general
mathematical theorems from differential geometry. In contrast our discussion
relies on simple and standard quantum mechanical concepts.
  The mathematical similarity of the physical problem at hand and that of a
phase-space path integral quantization scheme of a general classical system is
emphasized. Adopting this analogy in the general case leads to a general
quantization procedure that is invariant under general coordinate
transformations-- completely unlike any of the conventional quantization
prescriptions -- and therefore generalizes the concept of quantization to new
and hitherto inaccesible situations.
  In a complementary fashion , the so-obtained picture of general quantization
helps to derive useful semiclassical formulas for the Hall current in the case
of a filling factor equal to one for a general surface and magnetic field.
