Tight-binding investigation of the generalized Dirac comb

The problem of describing a negative spectrum of the periodic self-adjoint Schroedinger operator is very popular in quantum mechanics and it is called the tight-binding approximation. Our aim is to show that the main aspects of the theory are illustrated by a very simple one-dimensional example of minus the second derivative with arbitrary boundary conditions at the vertices of the lattice. We consider one-dimensional Schroedinger equation.