1210.4205 (Francisco M. Fernández et al.)

Critical parameters for quantum wells from a local approximation    [PDF]

Francisco M. Fernández, Javier Garcia

We apply the Riccati-Pad\'{e} method to one-dimensional quantum wells. The approach is based on a rational approximation to the logarithmic derivative of the wavefunction. We modify the Riccati-Pad\'{e} method and calculate accurate critical parameters for the Gaussian well and the Yukawa potential. The application of perturbation theory to a rational potentials yields interesting and baffling unphysical results.

View original: http://arxiv.org/abs/1210.4205