On a relation of bicomplex pseudoanalytic function theory to the complexified stationary Schrodinger equation

Using three different representations of the bicomplex numbers T congruent to Cl-C(1, 0) congruent to Cl-C(0, 1), which is a commutative ring with zero divisors defined by T = {w(0) + w(1)i(1) + w(2)i(2) + w(3)j vertical bar w(0), w(1), w(2), w(3) is an element of R} where i(1)(2) = -1, i(2)(2) = -1, j(2) = 1 and i(1)i(2) = j = i(2)i(1), we construct three classes of bicomplex pseudoanalytic functions. In particular, we obtain some specific systems of Vekua equations of two complex variables and we established some connections between one of these systems and the classical Vekua equations. We also consider the complexification of the real stationary two-dimensional Schrodinger equation. With the aid of any of its particular solutions, we construct a specific bicomplex Vekua equation possessing the following special property. The scalar parts of its solutions are solutions of the original complexified Schrodinger equation and the vectorial parts are solutions of another complexified Schrodinger equation.