Numerical matrix method for quantum periodic potentials

摘要

A numerical matrix methodology is applied to quantum problems with periodicpotentials. The procedure consists essentially in replacing the true potentialby an alternative one, restricted by an infinite square well, and in expressingthe wave functions as finite superpositions of eigenfunctions of the infinitewell. A matrix eigenvalue equation then yields the energy levels of theperiodic potential within an acceptable accuracy. The methodology has beensuccessfully used to deal with problems based on the well-known Kronig-Penney(KP) model. Besides the original model, these problems are a dimerized KPsolid, a KP solid containing a surface, and a KP solid under an external field.A short list of additional problems that can be solved with this procedure ispresented.