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Given a particular solution of a one-dimensional stationary Schroedingerequation (SE) this equation of second order can be reduced to a first orderlinear differential equation. This is done with the aid of an auxiliary Riccatiequation. We show that a similar fact is true in a multidimensional situationalso. We consider the case of two or three independent variables. Oneparticular solution of (SE) allows us to reduce this second order equation to alinear first order quaternionic differential equation. As in one-dimensionalcase this is done with the aid of an auxiliary Riccati equation. The resultingfirst order quaternionic equation is equivalent to the static Maxwell system.In the case of two independent variables it is the Vekua equation from theoryof generalized analytic functions. We show that even in this case it isnecessary to consider not complex valued functions only, solutions of the Vekuaequation but complete quaternionic functions. Then the first order quaternionicequation represents two separate Vekua equations, one of which gives ussolutions of (SE) and the other can be considered as an auxiliary equation of asimpler structure. For the auxiliary equation we always have the correspondingBers generating pair, the base of the Bers theory of pseudoanalytic functions,and what is very important, the Bers derivatives of solutions of the auxiliaryequation give us solutions of the main Vekua equation and as a consequence of(SE). We obtain an analogue of the Cauchy integral theorem for solutions of(SE). For an ample class of potentials (which includes for instance all radialpotentials), this new approach gives us a simple procedure allowing to obtainan infinite sequence of solutions of (SE) from one known particular solution

journal of physics. a, mathematical and general/journal of physics. a, mathematical and general

On the reduction of the multidimensional stationary Schrödinger equation to a first-order equation and its relation to the pseudoanalytic function theory