A pseudoCoulombian potential in D=1 dimensional space

Abstract

In the D = 1 dimensional space, we study the bound state solutions of the potential V(x) = −e x + b x2 (e, b > 0). They occur on the right half-plane x 2 [0,1[. In the limit b!0, we recover the spectrum of the D = 1 Coulomb potential. Supersymmetric properties are briefly discussed. The model is extended by considering complex coupling constants. Nonlinear effects are also treated by considering a linear energy dependence of the e coupling constant