Levinson theorem in two dimensions

A two-dimensional analogue of Levinson's theorem for nonrelativistic quantum mechanics is established, which relates the phase shift at threshold(zero momentum) for the $m$th partial wave to the total number of bound states with angular momentum $m\hbar(m=0,1,2,...)$ in an attractive central field.Comment: LaTeX, no figur

Anisotropic harmonic oscillator in a static electromagnetic field

A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneous static electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schr\"odinger equation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. In some of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherent and squeezed states and their time evolution are discussed in detail.Comment: revtex, 14 pages, no figure, two more references adde

Levinson theorem for Dirac particles in one dimension

The scattering of Dirac particles by symmetric potentials in one dimension is studied. A Levinson theorem is established. By this theorem, the number of bound states with even (odd) parity, $n_+$ ($n_-$), is related to the phase shifts $\eta_+(\pm E_k)$ [$\eta_-(\pm E_k)$] of scattering states with the same parity at zero momentum as follows: $$\eta_\pm(\mu)+\eta_\pm(-\mu)\pm{\pi\over 2}[\sin^2\eta_\pm(\mu) -\sin^2\eta_\pm(-\mu)]=n_\pm\pi.$$ The theorem is verified by several simple examples.Comment: REVTeX, 17 pages, no figur

On the partial wave amplitude of Coulomb scattering in three dimensions

The partial wave series for the Coulomb scattering amplitude in three dimensions is evaluated in a very simple way to give the closed result.Comment: revtex, 6 pages, no figur