Related papers: Functional treatment of quantum scattering via the…
The 2D space-fractional Schrodinger equation in the time-independent and time-dependent cases for the scattering problem in the fractional quantum mechanics is studied. We define and give the mathematical expression of the Green's functions…
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…
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
In this work we theoretically study properties of electric current driven by a temperature gradient through a quantum dot/molecule coupled to the source and drain charge reservoirs. We analyze the effect of Coulomb interactions between…
The most realistic situations in quantum mechanics involve the interaction between two or more systems. In the most of reliable models, the form and structure of the interactions generate differential equations which are, in the most of…
A quantum kinetic theory for correlated charged-particle systems in strong time-dependent electromagnetic fields is developed. Our approach is based on a systematic gauge-invariant nonequilibrium Green's functions formulation. We…
In this work a Green function approach for scattering quantum walks is developed. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression for arbitrary topologies and position dependent…
The definition of scattering operator in Quantum Field Theory is critically reconsidered. The correct treatment of one-particle states is connected with separation of selfaction from interaction. The formalism of functional integral is used…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
If a quantum mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an…
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
An exact solution for the scattering wavefunction from a nonlocal potential in the presence of Coulomb interaction is presented. The approach is based on the construction of a Coulomb Green's function in coordinate space whose associated…
A~dynamical justification of quantum differential cross section in the context of long time transition to stationary regime for the Schr\"odinger equation is suggested. The problem has been stated by Reed and Simon. Our approach is based on…
We consider a collision between a moving particle and a fixed system, each having internal degrees of freedom. We identify the regime where the motion of the particle acts as a work source for the joint internal system, leading to energy…
Conventional scattering theory is incomplete in that it does not adequately describe the behaviour of the wave function at macroscopic distances from the scattering reaction volume. In scattering experiments particles are incident from…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
An analysis of the Schwinger's action principle in Lagrangian quantum field theory is presented. A solution of a problem contained in it is proposed via a suitable definition of a derivative with respect to operator variables. This results…
Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional time Schr\"odinger equation (SE), which differs from the standard SE by the…
Integral form of the space-time-fractional Schr\"odinger equation for the scattering problem in the fractional quantum mechanics is studied in this paper. We define the fractional Green's function for the space-time fractional Schrodinger…