Eigenvalues, Eigenfunctions and Green’s Functions on a Path via Chebyshev Polynomials
نویسندگان
چکیده
In this work we analyze the boundary value problems on a path associated with Schrödinger operators with constant ground state. These problems include the cases in which the boundary has two, one or none vertices. In addition, we study the periodic boundary value problem that corresponds to the Poisson equation in a cycle. Moreover, we obtain the Green’s function for each regular problem and the eigenvalues and their corresponding eigenfunctions otherwise. In each case, the Green’s functions, the eigenvalues and the eigenfunctions are given in terms of first, second and third kind Chebyshev polynomials.
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