Visualizing Non-Asymptotic Quantum Scattering from a Separable Potential

Kay-Kong Wan, R. G. McLean

Jared R. Stenson, Albert W. Stetz

Beginning with the conventional asymptotic description of quantum scattering, we propose a simple wave function that is valid at all distances and compute the corresponding Bohmian trajectories. This 'simulated experiment' allows a concrete visualization of the process throughout the scattering interaction. Not only is this of pedagogic value at the undergraduate level, it also illustrates several important themes in time-dependent scattering theory, such as the importance of wave packets, the role of cross sections in describing measurement and the wave and particle pictures of quantum mechanics.

J. M. Combes

F. Cannata, J.-P. Dedonder, Alberto Ventura

A general formalism is worked out for the description of one-dimensional scattering in non-hermitian quantum mechanics and constraints on transmission and reflection coefficients are derived in the cases of P, T, or PT invariance of the Hamiltonian. Applications to some solvable PT-symmetric potentials are shown in detail. Our main original results concern the association of reflectionless potentials with asymptotic exact PT symmetry and the peculiarities of separable kernels of non-local potentials in connection with hermiticity, T invariance and PT invariance.

S. Brandt, Hans Dieter Dahmen

N. Grama, Cornelia Grama, Ioan Zamfirescu

An Ansatz based on an etalon function generated by the problem itself is used in order to obtain a uniform asymptotic approximation of the 3D wave function for the scattering by a non-central potential.The obtained uniform asymptotic approximation removes the singularities at the caustics that occur in the 3D WKB approximation.The scattering amplitude provided by the uniform asymptotic approximation contains the poles that are the fingerprints of the system.The comparison of the obtained uniform asymptotic approximation of the 3D scattering wave function with the exact scattering wave function shows the versatility of the Ansatz based on an etalon function generated by the problem itself.