Quantum Mechanical Scattering Research Articles

Theory of Quantum Mechanical Scattering in Hyperbolic Space

The theory of quantum mechanical scattering in hyperbolic space is developed. General formulas based on usage of asymptotic form of the solution of the Shrödinger equation in hyperbolic space are derived. The concept of scattering length in hyperbolic space, a convenient measurable in describing low-energy nuclear interactions is introduced. It is shown that, in the limit of the flat space, i.e., when ρ→∞, the obtained expressions for quantum mechanical scattering in hyperbolic space transform to corresponding formulas in three-dimensional Euclidean space.

Quantum-Mechanical Scattering Problem in Lobachevsky Space at Low Energies

Based on the use of the asymptotics for the wave function of a scattered particle in a Lobachevsky space in a form close to the asymptotics in flat space, general formulas for the theory of quantum mechanical scattering in this space are derived. This approach makes it possible to represent the basic formulas of the theory of scattering in the Lobachevsky space in the form that coincides with the corresponding expressions in three-dimensional Euclidean space. We o.er quantities (length of scattering, effective scattering radius), that are used in describing scattering at short-range potentials and are convenient as phenomenological parameters in describing nuclear interactions at low energies. Numerical estimates of these quantities and cross sections at low energies, that are characteristic of nuclear physics, are given.

On the Quantum Mechanical Scattering Statistics of Many Particles

The probability of a quantum particle being detected in a given solid angle is determined by the S-matrix. The explanation of this fact in time-dependent scattering theory is often linked to the quantum flux, since the quantum flux integrated against a (detector-) surface and over a time interval can be viewed as the probability that the particle crosses this surface within the given time interval. Regarding many particle scattering, however, this argument is no longer valid, as each particle arrives at the detector at its own random time. While various treatments of this problem can be envisaged, here we present a straightforward Bohmian analysis of many particle potential scattering from which the S-matrix probability emerges in the limit of large distances.

A New Spherical Bessel Function Result Related to Quantum Mechanical Scattering Theory

The authors present a derivative formula for the square of a spherical Bessel function in terms of the spherical Bessel function of twice the argument. This derivative formula is then applied in an inversion problem for the partial-wave Born approximation in quantum mechanical scattering theory. Several other closely related results and derivative formulas are also considered.

Quantum Mechanical Scattering of Asymmetric Molecules. II. Comparison between the Systems He–D2 and He–HT

Exact quantum mechanical coupled channel calculations have been performed in order to compare the rotating potential model for heteronuclear molecules with an asymmetric mass distribution, and the usual potential with anisotropy terms for homonuclear molecules. The scattering cross sections of He–D2 and He–HT show no difference in shape, apart from some quenching of the orbiting resonances. There is, however, a significant difference in absolute magnitude, due predominantly to inelastic processes. In the inelastic cross sections, the effect of the shift of the center of mass from the center of interaction in asymmetric molecules counteracts the effect of a change in moment of inertia.

A Simplified Treatment of the Quantum-Mechanical Scattering Problem Using Wave Packets

This paper presents a treatment of quantum-mechanical scattering suitable for a senior level course in modern physics. The entire treatment is based on the use of wave packets instead of unrealistic plane waves. The asymptotic behavior of the scattered wave packet is derived from physical considerations, and the Born approximation is then obtained for a wave packet in a manner which displays the details of the scattering process.