The Kronig - Penney model extended to arbitrary potentials via numerical matrix mechanics

Kronig-Penney model has always been a starting point to study periodic potentials for physics students. In this study, The matrix diagonalization method to obtain the solution of Schrödinger (eigenvalue) equation for the non-periodic Kronnig Penney like potentials is explained.Then, by introducing Kronig Penney model and Bloch theorem the solution of the periodic potentials is discussed. Finally, the solutions of periodic potentials is described using matrix diagonalization method with Fortran and the results has been shown graphically.