Ground states of continuum models

Oscar Bolina

Kaplan Shinyway Overseas Pathway College,

We calculate the ground state energies of a system of electrons in one-dimensional infinitely deep square well potentials. We analyze the cases when the wells are regularly spaced and when they are clustered together to form one single large well. These potentials are intended to physically describe the interaction of electrons and nuclei in a continuum model. We investigate which potential yields the minimum ground state energy using elements of interpolation potential in quantum mechanics derived from first principles. We also mention models of crystalline formation that are related to this problem. PACS { 73.21.Fg, 73.22 Dj