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The quantum dynamics of a two-dimensional charged spin $1/2$ particle isstudied for general, symmetry--free curved surfaces and general, nonuniformmagnetic fields that are, when different from zero, orthogonal to the definingtwo surface. Although higher Landau levels generally lose their degeneracyunder such general conditions, the lowest Landau level, the ground state,remains degenerate. Previous discussions of this problem have had lessgenerality and/or used supersymmetry, or else have appealed to very generalmathematical theorems from differential geometry. In contrast our discussionrelies on simple and standard quantum mechanical concepts.  The mathematical similarity of the physical problem at hand and that of aphase-space path integral quantization scheme of a general classical system isemphasized. Adopting this analogy in the general case leads to a generalquantization procedure that is invariant under general coordinatetransformations-- completely unlike any of the conventional quantizationprescriptions -- and therefore generalizes the concept of quantization to newand hitherto inaccesible situations.  In a complementary fashion , the so-obtained picture of general quantizationhelps to derive useful semiclassical formulas for the Hall current in the caseof a filling factor equal to one for a general surface and magnetic field.Comment: 32, Phys. Rev. A, 48, 253

Landau-level ground-state degeneracy and its relevance for a general quantization procedure