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Pseudoanalytic function theory is considered to study a two-dimensionalsupersymmetric quantum mechanics system. Hamiltonian components of thesuperhamiltonian are factorized in terms of one Vekua and one Bers derivativeoperators. We show that imaginary and real solutions of a Vekua equation andits Bers derivative are ground state solutions for the superhamiltonian. Thetwo-dimensional Darboux and pseudo-Darboux transformations correspond to Bersderivatives in the complex plane. Results on the completeness of the groundstates are obtained. Finally, superpotential is studied in the separable casein terms of transmutation operators. We show how Hamiltonian components of thesuperhamiltonian are related to the Laplacian operator using thesetransmutation operators.

On two-dimensional supersymmetric quantum mechanics, pseudoanalytic functions and transmutation operators