Numerical matrix method for quantum periodic potentials

Abstract

A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the wave functions as finite superpositions of eigenfunctions of the infinite well. A matrix eigenvalue equation then yields the energy levels of the periodic potential within an acceptable accuracy. The methodology has been successfully used to deal with problems based on the well-known Kronig-Penney (KP) model. Besides the original model, these problems are a dimerized KP solid, 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 is presented.

arXiv comment9 pages, 12 figures, Ref. 9 differs from the one appearing in the AJP paper

References in corpus (4)

• The Harmonic Oscillator in Quantum Mechanics: A Third Way
• The Kronig-Penney model extended to arbitrary potentials via numerical matrix mechanics
• Numerical matrix method for quantum periodic potentials
• Solving for three-dimensional central potentials using matrix mechanics

Cited by in corpus (5)

• Numerical matrix method for quantum periodic potentials
• Theoretical Prediction of Enhanced Thermopower in n-doped Si/Ge Superlattices using Effective Mass Approximation
• Quantum matrix diagonalization visualized
• Attractive Kronig-Penney Band Structures and Wave Functions
• Edge Localized Schrödinger Cat States in Finite Lattices via Periodic Driving