Pauli equation and the method of supersymmetric factorization

We consider different variants of factorization of a 2 x 2 matrix Schroedinger/Pauli operator in two spatial dimensions. They allow us to relate its spectrum to the sum of spectra of two scalar Schroedinger operators, in a manner similar to one-dimensional Darboux transformations. We consider both the case when such factorization is reduced to the ordinary two-dimensional supersymmetric quantum mechanics quasifactorization and a more general case which involves covariant derivatives. The admissible classes of electromagnetic fields are described and some illustrative examples are given