Initial-Boundary Value Problem for Schrödinger Equation on Ladder-Type Graph

In the present paper, we obtained integral representation of solutions for initial-boundary value problems (IBVP) for the Schrödinger equation on ladder-type graphs using the Fokas method. This method uses special generalization of the Fourier transformation, called the unified transformation. Obtained solutions representation of the problem for ladder-type graphs let us to see exactly the parts that correspond transmission, reflection and trapping part of the wave at the branching point of the graphs. The solutions to the problems are constructed by the so-called Fokas method, which is a generalization of the Fourier transform method. In this case, the problem is reduced to a system of algebraic equations for the Fourier transform of the unknown values of the solution at the vertices of the graph.