Related papers: Relation between scattering amplitude and Bethe-Sa…
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We will obtain the potential scattering amplitude form the complete Green function in the corresponding…
Medium modification of scattering properties in interacting Bose systems are considered by solving the Bethe-Salpeter equation. An equation of state for the normal phase (generalized Beth-Uhlenbeck formula) is given using the in-medium…
Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details…
The effective field theory approach is applied to the three-nucleon process of $S=1/2$ neutron-deuteron scattering in the S-wave, including the effective range parameters summed at all orders. This is achieved through a modification of the…
We present a theoretical analysis of excitation modes in Bose-Einstein condensates in ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We assume that…
Resonances are of particular importance to the scattering of composite particles in quantum mechanics. We build an effective field theory for two-body scattering which includes a low-energy $S$-wave resonance. Our starting point is the most…
A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape an explicit analytical…
On-shell scattering amplitudes have proven to be useful tools for tackling the two-body problem in general relativity. This thesis outlines how to compute relevant classical observables that are themselves on-shell, directly from…
The present paper generalizes preceding papers of the author and opens a cycle of works concerning the general posing and solution in analytic form of the quantum-mechanical inverse scattering problem (for a given partial channel) in a…
The method of effective field theories (EFTs) is developed for the scattering of two particles at wavelengths which are large compared to the range of their interaction. It is shown that the renormalized EFT is equivalent to the effective…
We provide the two fundamental sets of functional relations which describe the strong coupling limit of scattering amplitudes in $\mathcal{N} = 4$ SYM dual to Wilson loops in $AdS_3$: the basic $QQ$-system and the derived $TQ$-system. We…
Within the framework of potential scattering theory we derive an analytical two-potential formula for the on-shell partial wave scattering amplitude. This formula embodies a large number of possible applications, including long range…
The scattering solutions of the one-dimensional Schrodinger equation for the Woods-Saxon potential are obtained within the position-dependent mass formalism. The wave functions, transmission and reflection coefficients are calculated in…
The physical information encoded in the cosmological late-time wavefunction of the universe is tied to its singularity structure and its behaviour as such singularities are approached. One important singularity is identified by the…
The problem of calculating of the mass spectrum of the two-body Bethe-Salpeter equation is studied with no reduction to the three-dimensional ("quasipotential") equation. The method to find the ground state and excited states for a channel…
We present an investigation of various gauge invariant definitions of the $q\bar q$ Bethe-Salpeter (BS) amplitude for mesons in lattice QCD, and compare them to the Coulomb and Landau gauge BS amplitudes. We show that the gauge invariant BS…
We study the dispersive behaviors of two-particles Schr\"odinger and wave equations in the Aharonov-Bohm field. In particular, we prove the Strichartz estimates for Schr\"odinger and wave equations in this setting. The key point is to…
We develop a formalism for computing the scattering amplitudes in maximally symmetric de Sitter spacetime with compact spatial dimensions. We describe quantum states by using the representation theory of de Sitter symmetry group and link…
If $A_q(\beta, \alpha, k)$ is the scattering amplitude, corresponding to a potential $q\in L^2(D)$, where $D\subset\R^3$ is a bounded domain, and $e^{ik\alpha \cdot x}$ is the incident plane wave, then we call the radiation pattern the…
Nuclear effective field theory is applied to the effective range expansion of S-wave nucleon-nucleon scattering on a discrete lattice. Lattice regularization is demonstrated to yield the effective range expansion in the same way as in the…