BOUNDARY LEAST-SQUARES METHOD FOR THE SOLUTION OF SCHRODINGERS EQUATION IN QUANTUM WIRES

We present a method for the approximate semianalytical calculation of wave functions and eigenenergies in systems consisting of domains with known bulk solutions of tile corresponding Schrodinger equation (e.g. with piecewise constant potential). The trial wave function is writte n as a normalized linear combination of several bulk solutions for the given energy. The coefficients of the linear combination are found by minimization of the integral of square mismatch along the boundaries. Mathematically the problem is equivalent to the minimization of the R ayleigh quotient or solution of the generalized eigenproblem for tile vector of coefficients. The value of the residual provides an estimati on of tile accuracy of the results and gives the possibility to choose an optimal set of trial functions. We illustrate the use of the metho d by calculation of eigenfunctions of infinitely long triangular and q uadrilateral wires.