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

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

Nonlocal electrodynamics in 2+1 dimensions from Chern-Simons theory

The theory of a spinor field interacting with a pure Chern-Simons gauge field in 2+1 dimensions is quantized. Dynamical and nondynamical variables are separated in a gauge-independent way. After the nondynamical variables are dropped, this theory reduces to a pure spinor field theory with nonlocal interaction. Several two-body scattering processes are studied and the cross sections are obtained in explicitly Lorentz invariant forms.Comment: LaTeX, no figur

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

Levinson theorem for Dirac particles in two dimensions

The Levinson theorem for nonrelativistic quantum mechanics in two spatial dimensions is generalized to Dirac particles moving in a central field. The theorem relates the total number of bound states with angular momentum $j$ ($j=\pm 1/2, \pm 3/2, ...$), $n_j$, to the phase shifts $\eta_j(\pm E_k)$ of scattering states at zero momentum as follows: $\eta_j(\mu)+\eta_j(-\mu)= n_j\pi$.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

Nonlocal scalar electrodynamics from Chern-Simons theory

The theory of a complex scalar interacting with a pure Chern-Simons gauge field is quantized canonically. Dynamical and nondynamical variables are separated in a gauge-independent way. In the physical subspace of the full Hilbert space, this theory reduces to a pure scalar theory with nonlocal interaction. Several scattering processes are studied and the cross sections are calculated.Comment: REVTeX, no figur

Electron-positron pair creation in a vacuum by an electromagnetic field in 3+1 and lower dimensions

We calculate the probability of electron-positron pair creation in vacuum in 3+1 dimensions by an external electromagnetic field composed of a constant uniform electric field and a constant uniform magnetic field, both of arbitrary magnitudes and directions. The same problem is also studied in 2+1 and 1+1 dimensions in appropriate external fields and similar results are obtained.Comment: REVTeX, 10 pages, no figure, a brief note and some more references added in the proo