Related papers: Three-body Forces in Oscillator Bases Expansion
This work introduces a unified emulation framework for studying continuum physics in finite quantum systems. Using a reduced basis method, we construct powerful emulators for the inhomogeneous Schr\"{o}dinger equation that operate in a…
We use the "tridiagonal representation approach" to solve the time-independent Schr\"odinger equation for the bound states of generalized versions of the trigonometric and hyperbolic P\"oschl-Teller potentials. These new solvable potentials…
When dealing with satellites orbiting a central body on a highly elliptical orbit, it is necessary to consider the effect of gravitational perturbations due to external bodies. Indeed, these perturbations can become very important as soon…
We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem becomes non-perturbative at momenta of the order of the inverse of the two-body scattering length, and an infinite number of graphs…
We study the classical electrodynamics of extended bodies. Currently, there is no self-consistent dynamical theory of such bodies in the literature. Electromagnetic energy-momentum is not conserved in the presence of charge and some…
In this work, we prove global well-posedness and scattering for systems of quadratic nonlinear Schr\"odinger equations in the critical three-dimensional case, for small, localized data. For the terms corresponding to the nonlinearity…
We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schr\"odinger algebras which relies on a particular subalgebra of the four-dimensional relativistic conformal algebra. In particular, we reproduce the…
The universal variational expansion for the non-relativistic three-body systems is explicitly constructed. Three-body universal expansion can be used to perform highly accurate numerical computations of the bound state spectra in arbitrary…
The semiclassical Schr\"odinger equation with time-dependent potentials is an important model to study electron dynamics under external controls in the mean-field picture. In this paper, we propose two multiscale finite element methods to…
This paper is devoted to the analysis of propagation properties for the solutions of a one-dimensional non-local Schr\"odinger equation involving the fractional Laplace operator $(-d_x^2)^s$, $s\in(0,1)$. We adopt a classical WKB approach…
Three-body systems of scalar bosons are described in the framework of relativistic constraint dynamics. With help of a change of variables followed by a change of wave function, two redundant degrees of freedom get eliminated and the…
The semiclassical Schr\"{o}dinger equation with multiscale and random potentials often appears when studying electron dynamics in heterogeneous quantum systems. As time evolves, the wavefunction develops high-frequency oscillations in both…
The solution of the hyperangular Schr\"odinger equation for few-body systems using a basis of explicitly correlated Gaussians remains numerically challenging. This is in part due to the number of basis functions needed as the system size…
This work reviews recent advances in the analytical treatment of the continuum spectrum of correlated few-body non-relativistic Coulomb systems. The exactly solvable two-body problem serves as an introduction to the non-separable…
Progress toward the solution of the strongly correlated electron problem has been stymied by the exponential complexity of the wave function. Previous work established an exact two-body exponential product expansion for the ground-state…
In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this…
We define Sturmian basis functions for the harmonic oscillator and investigate whether recent insights into Sturmians for Coulomb-like potentials can be extended to this important potential. We also treat many body problems such as coupling…
We derive exact expressions for the scalar and electromagnetic self-forces and self-torques acting on arbitrary static extended bodies in arbitrary static spacetimes with any number of dimensions. Non-perturbatively, our results are…
Effective field theories (EFTs) are widely used to study many-body systems by describing two-body interactions using zero-ranged contact potentials. However, when extended to three-body processes, these contact interactions lead to…
We consider the functional Schrodinger equation for a self interacting scalar field in an expanding geometry. By performing a time dependent scale transformation on the argument of the field we derive a functional Schrodinger equation whose…