Related papers: Exact Green's function for rectangular potentials …
Green function (which can be called the q-analogous of the Hankel function) on the quantum plane E_q^2= E_q(2)/U(1) is constructed.
Single-particle resonances in the continuum are crucial for studies of exotic nuclei. In this study, the Green's function approach is employed to search for single-particle resonances based on the relativistic-mean-field model. Taking…
A new approach proposed recently by author for the calculation of Green functions in quantum field theory and quantum mechanics is briefly reviewed. The method is applied to nonperturbative calculations for anharmonic oscillator,…
The Fast Multipole Method (FMM) obeys periodic boundary conditions "natively" if it uses a periodic Green function for computing the multipole expansion in the interaction zone of each FMM oct-tree node. One can define the "optimal" Green…
The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…
Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function.…
An infinite sequence of potential well functions is considered. A numerical method is used for the Schr$\ddot{\text{o}}$dinger equation to obtain the energy eigenvalue spectra for a number of these potential well functions. The results for…
Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic…
A new perspective of the Green's function in a boundary value problem as the only eigenstate in an auxiliary formulation is introduced. In this treatment, the Green's function can be perceived as a defect state in the presence of a…
For a three-electron system with finite-strength interactions confined to a one-dimensional harmonic trap, we solve the Schroedinger equation analytically to obtain the exact solutions, from which we construct explicitly the simultaneous…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
The Dyson-Schwinger (DS) equations for a quantum field theory in $D$-dimensional space-time are an infinite sequence of coupled integro-differential equations that are satisfied exactly by the Green's functions of the field theory. This…
Covariant relativistic quantum theory is used to study the covariant Green's function, which can be used to determine the proper time evolved wave functions that are solutions to the covariant Schr\"odinger type equation for a massive spin…
We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on $\mathbb{Z}^d$ with certain slowly decaying long-range hopping and analytic cosine type potentials. As applications, we prove the…
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…
The Green's functions for the Laplace equation respectively satisfying the Dirichlet and Neumann boundary conditions on the upper side of an infinite plane with a circular hole are introduced and constructed. These functions enables…
Many physics problems have $J(x)=L(x)E(x)+h(x)$, source $h(x)$, fields $E$,$J$ satisfying differential constraints, symbolized by $E\in\cal E$,$J\in\cal J$ where $\cal E$,$\cal J$ are orthogonal spaces. If $L(x)$ takes values in certain…
Practical methods to compute dipole strengths for a three-body system by using a discretized continuum are analyzed. New techniques involving Green's function are developed, either by correcting the tail of the approximate wave function in…
A completely antisymmetrized Green's function approach to the inclusive quasielastic $(e,e')$ scattering, including a realistic one-body density, is presented. The single particle Green's function is expanded in terms of the eigenfunctions…
A novel scheme to solve the quantum eigenvalue problem through the imaginary-time Green function Monte Carlo method is presented. This method is applicable to the excited states as well as to the ground state of a generic system. We…