Inverse Problems in Fermion Systems

Antonio S. de Castro

The problem of a fermion subject to a a scalar inversely linear potential in a two‐dimensional world is mapped into a Sturm‐Liouville problem for nonzero eigenenergies. This mapping gives rise to an effective Kratzer potential and exact bounded solutions are found in closed form. The normalizable zero‐eigenmode solution is also found. A few unusual results are revealed.

De Castro, A S

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background potential. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength.

Leon N. Cooper

S. Pruski

Joel Feldman, Eugene Trubowitz B