Continuity of Bound and Unbound States in a Fermi Gas: A Soluble Example
Abstract
Considering a gas of independent fermions in the presence of an attractive localized potential, one can show that the properties of the system as a whole are smooth (analytic) functions of the strength parameter of the potential, even at those values where new singleparticle bound states appear. Thus for the system as a whole, the transition from ``unbound'' to ``bound'' states is continuous and the concept of a bound state cannot be made precise. This is illustrated here for a simple mathematically soluble model—noninteracting spinless fermions moving in the presence of a deltafunction potential in one dimension. Some related physical ideas are also presented.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 April 1966
 DOI:
 10.1063/1.1704982
 Bibcode:
 1966JMP.....7..682M