Simulation Study of Arbitrary 1D Periodic Potentials by Modified Marsiglio’s Matrix Approach using Gnumeric Spreadsheet

In this paper, we present a structured approach to solving the quantum mechanical problem of a particle in 1D periodic square well potential to obtain energy eigenvalues. Here, we utilize the modified Marsiglio’s matrix mechanics method to obtain energy eigenvalues for the potential. The method is implemented in a Gnumeric spreadsheet environment, a free open source software that has an in-built eigensolver, to gain clarity regarding each of the steps involved by choosing a smaller-sized H-matrix. The resultant eigenvalues obtained using the simulation are plotted with respect to k values to visualize the band structure diagrams arising from various periodic potentials such as a harmonic oscillator, inverted harmonic oscillator, and linear well potential. This implementation strategy helps us study the physical system in a more systematic and simpler way, pedagogically.