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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

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.

Neutral fermions of spin 1 2 with magnetic moment can interact with electromagnetic fields through nonminimal coupling. In 2+1 dimensions the electromagnetic field strength plays the same role to the magnetic moment as the vector potential to the electric charge. This duality enables one to obtain physical results for neutral particles from known ones for charged particles. We give the probability of neutral particle-antiparticle pair creation in the vacuum by non-uniform electromagnetic fields produced by constant uniform charge and current densities.