Confinement properties for the Dirac equation with scalar-like and vector-like potentials

The (1+3)- and (1+1)-dimensional Dirac equation with both scalar-like and vector-like potentials is discussed. The authors prove that if the scalar-like potential is just equal to the vector-like potential, the confinement is impossible, i.e. there must be scattering states. Two exact solutions with linear potential and harmonic oscillator potential in this condition are given.