Related papers: A generalized scattering theory in quantum mechani…
Using a representation of multichannel quantum defect theory in terms of a quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show, that…
It is shown that the Stone-von Neumann theorem is inapplicable to scattering a quantum nonrelativistic particle on a one-dimensional "short-range" potential barrier, since the unboundedness of the position operator plays here a crucial…
This study concerns the two-body scattering of particles in a one-dimensional periodic potential. A convenient ansatz allows for the separation of center-of-mass and relative motion, leading to a discrete Schr\"odinger equation in the…
This work presents an extensive exploration of scattering and tunneling involving composite objects with intrinsic degrees of freedom. We aim at exact solutions to such scattering problems. Along this path we demonstrate solution to model…
The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to…
We describe the bound state and scattering properties of a quantum mechanical particle in a scalar $N$-prong potential. Such a study is of special interest since these situations are intermediate between one and two dimensions. The energy…
We survey the basic notions of scattering theory in Hamiltonian mechanics with a particular attention to the analogies with scattering theory in quantum mechanics. We discuss the scattering symplectomorphism, which is analogous to the…
We put forward a finite theory of quantum scattering of fundamental particles without using auxiliary particles. It suggests that to avoid ultraviolet divergencies and model faster-than-light effects it suffices to appropriately change only…
A theoretical method for treating collisions in the presence of multiple potentials is developed by employing the Schwinger variational principle. The current treatment agrees with the local (regularized) frame transformation theory and…
Multi-particle scattering states are constructed for massive Wigner particles in the general operator-algebraic setting of wedge-local quantum field theory. The apparent geometrical restriction of the conventional wedge-local Haag-Ruelle…
A simple and explicit technique for the numerical solution of the two-particle, time-dependent Schr\"{o}dinger equation is assembled and tested. The technique can handle interparticle potentials that are arbitrary functions of the…
A generalized scattering amplitude where momenta of incoming-particles and outgoing-particles as well as positions of incoming-particles and outgoing-particles are specified is formulated. Idealistic beams and idealistic measuring…
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain…
To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of…
The simple form of the optical theorem of scattering theory, $\sigma_{\rm tot}^{\rm pw} = (4\pi/k)\,\Im f(0)$, is valid for an incident plane wave or for a wave packet whose Fourier components possess azimuthal symmetry about the incident…
The last few years have seen rapid development of applications of quantum computation to quantum field theory. The first algorithms for quantum simulation of scattering have been proposed in the context of scalar and fermionic theories,…
We give a method of describing thermodynamical transport phenomena, based on a quantum scattering theoretical approach. We consider a quantum system of particles connected to thermodynamical reservoirs by leads. The effects of the…
We give a new sufficient condition for existence and completeness of wave operators in abstract scattering theory. This condition generalises both trace class and smooth approaches to scattering theory. Our construction is based on…
The generalized Klein-Nishina formula for Compton scattering of charged particles by a finite train of pulses is derived in the framework of quantum electrodynamics. The formula also applies to classical Thomson scattering provided that…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…