6,680 research outputs found
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 th partial wave to the total number of bound states with
angular momentum 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
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, (), is related to the phase
shifts [] of scattering states with the same
parity at zero momentum as follows: The theorem is
verified by several simple examples.Comment: REVTeX, 17 pages, no figur
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