An expression for the sum of the position-probability densities for a one-dimensional system of fermions in the ground state is derived from wave mechanics. Its accuracy in application to three different potential-energy functions is shown. For the square well of infinite height it preserves the sinusoidal contributions which disappear in the corresponding Fermi—Thomas treatment. Where the potential energy exceeds the Fermi level, it is properly characterized.
No takes yet. Share an insight, caveat, or question.
Herbert Payne (1963) studied this question.
Synapse has enriched 4 closely related papers on similar clinical questions. Consider them for comparative context: