Schrödinger Equation with Periodic potentials

This book talks about Schrödinger equation with periodic potential U(x), which has a multiwell structure with many wells of di¿erent depth. We have calculated the solutions for both low and higher energies, and they are very sensitive. The interesting of this book is we have found localized solutions for the energies that are greater than the max(U(x)). The localized solutions are localized around the minima of the local maxima of the potential. We found these solutions only for a few values of the energies that are slightly higher than max(U(x)). For these solutions, we found bands of forbidden momenta. We have also studied the Wigner and and Weyl functions corresponding to solutions of Schrödinger equation (for both cases of energy smaller and greater than the maximum value of the potential). The Wigner and Weyl functions con¿rms our results in the case of localized solutions and the bands of forbidden momenta.