Energy levels of atomic hydrogen in a closed box: A natural cutoff criterion of the electronic partition function

Abstract

The radial part of the Schrodinger equation for atomic hydrogen in a spherical box of radius is numerically solved. Two sets of energy levels are obtained, the first one reproduces the unperturbed bound levels up to a given principal quantum number while the other one unbound describes levels with energy greater than the unperturbed ionization energy of atomic hydrogen EH. These last levels asymptotically converge to the corresponding set which can be obtained by the particle in the box model, i.e., levels which increase their energy as n2 thus ensuring the convergence of the electronic partition function.