Effects of the boundary conditions in the problem of a quantum well under electric field

The theory of a quantum well in an applied electric field is discussed with emphasis on the model one adopts to describe the effect of the field outside the well. This depends on just one parameter which measures the asymptotic boundary condition one imposes outside the well in the domain where the electrostatic potential sinks. The discussion is carried in parallel in terms of wavefunctions and Green functions. It is found that extreme changes in the boundary conditions do not affect significantly the eigenvalues of the well states up to the highest electric fields attained in practice.