# ExtendedKronigPennyMatrix

Documentation for ExtendedKronigPennyMatrix.

# Introduction

Construct a numerical Hamiltonian matrix $(h_{nm})$ of Kronig-Penny model extended to arbitrary potentials based on the paper written by Pavelich and Marsiglio.

\[\sum_{m=1}^{\infty} h_{nm} c_{m} = ec_{n}\]

Energy is expressed in units of $E_{1}^{(0)}$.

\[E_{1}^{(0)} = \dfrac{\pi^2\hbar^2}{2ma^2}\]

Refer the formulations to the following paper:

R. L. Pavelicha and F. Marsigliob, "The Kronig-Penney model extended to arbitrary potentials via numerical matrix mechanics," American Journal of Physics 83, 774 (2015). DOI:10.1119/1.4923026, ResearchGate