Related papers: An efficient and accurate method to obtain the ene…
It is shown that if a complete set of mutually commuting operators is formed by constants of motion, then, up to a factor that only depends on the time, each common eigenfunction of such operators is a solution of the Schr\"odinger…
It is shown that in a scalar quantum field theory at high temperatures we can compute even time dependent observables from an effective theory, which can be interpreted as a (nonlocal) classical statistical field theory. We examine the…
We reexamine the general solution of a Schr\"{o}dinger equation in the presence of a time-dependent linear potential in configuration space based on the Lewis-Riesenfeld framework. For comparison, we also solve the problem in momentum space…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
We study exact solutions of Dirac and Klein-Gordon equations and Green functions in d-dimensional QED and in an external electromagnetic field with constant and homogeneous field invariants. The cases of even and odd dimensions are…
The time-dependent variational principle proposed by Balian and Veneroni is used to provide the best approximation to the generating functional for multi-time Green's functions of a set of (bosonic) observables $Q_{\mu)$. By suitably…
Characterizing distinct electron wave packets is a basic task for solid-state electron quantum optics with applications in quantum metrology and sensing. A important circuit element for this task is a non-stationary potential barrier than…
The time-dependent Schrodinger equation is solved for two model problems for a non-Hermitian quantum system.A simple matrix model system is used to examine two critical problems for these systems: complex and non-observable energies and…
A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of…
We derive expressions for the expectation values of the local energy and the local power transferred by an external electrical field to a many-particle system of interacting spinless electrons. In analogy with the definition of the (local)…
In this paper, we summarize the technique of using Green functions to solve electrostatic problems. We start by deriving the electric potential in terms of a Green function and a charge distribution. We then provide a variety of example…
In quantum mechanics, the time evolution of particles is given by the Schr\"odinger equation. It is valid in a nonrelativistic regime where the interactions with the particle can be modelled by a potential and quantised fields are not…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
We use time-independent canonical transformation methods to discuss the energy eigenfunctions for the simple linear potential, pedagogically setting the stage for some field theory calculations to follow. We then discuss the Schr\"odinger…
Theoretical approaches to the photoionization of few-electron atoms are discussed. These include nonequilibrium Greens functions and wave function based approaches. In particular, the Multiconfiguration Time-Dependent Hartree-Fock method is…
By using the multipolar gauge it is shown that the quantum mechanics of an electrically charged particle moving in a prescribed classical electromagnetic field (wave mechanics) may be expressed in a manner that is gauge invariant, except…
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…
The magnon Hedin's equations are derived via the Schwinger functional derivative technique, and the resulting self-consistent Green's function method is used to calculate ground state spin patterns and magnetic structure factors for…
This paper discusses the technical aspects - mathematical and numerical - associated with the numerical simulations of a mesoscopic system in the time domain (i.e. beyond the single frequency AC limit). After a short review of the state of…