Solution of the equation d/dx(pdu/dx)+qu=cu by a solution of the equation d/dx(pdu/dx)+qu=0

Details Solution of the equation d/dx(pdu/dx)+qu=cu by a solution of the equation d/dx(pdu/dx)+qu=0 Solution of the equation d/dx(pdu/dx)+qu=cu by a solution of the equation d/dx(pdu/dx)+qu=0

2007-08-16

arxiv.org/abs/0708.2271v2

Published under the title: A representation for solutions of the Sturm-Liouville equation. Complex Variables and Elliptic Prob

Physics

Mathematical Physics

Scientific paper

We give a simple solution of the equation d/dx(pdu/dx)+qu=cu whenever a nontrivial solution of d/dx(pdu/dx)+qu=0 is known. The method developed for obtaining this result is based on the theory of pseudoanalytic functions and their relationship with solutions of the stationary two-dimensional Schrodinger equation. The final result, that is the formula for the general solution of the equation d/dx(pdu/dx)+qu=cu has a simple and easily verifiable form.

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