Related papers: Solving the Dirac equation with nonlocal potential…
Starting from a time-dependent Schr\"odinger equation, stationary states of 3D central potentials are obtained. An imaginary-time evolution technique coupled with the minimization of energy expectation value, subject to the orthogonality…
The importance of the energy spectrum of bound states and their restrictions in quantum mechanics due to the different methods have been used for calculating and determining the limit of them. Comparison of Schrodinger-like equation…
By constructing the commutative operators chain, we derive the integrable conditions for solving the eigenfunctions of Dirac equation and Schr\"odinger equation. These commutative relations correspond to the intrinsic symmetry of the…
In this paper, we study an infeasible interior-point method for linear optimization with full-Newton step. The introduced method uses an algebraic equivalent transformation on the centering equation of the system which defines the central…
An efficient method, preconditioned conjugate gradient method with a filtering function (PCG-F), is proposed for solving iteratively the Dirac equation in 3D lattice space for nuclear systems. The filtering function is adopted to avoid the…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
Coefficient inverse problems related to identifying the right-hand side of an equation with use of additional information is of interest among inverse problems for partial differential equations. When considering non-stationary problems,…
We present a version of the T-moves approach for treating nonlocal pseudopotentials in diffusion Monte Carlo which has much smaller time-step errors than the existing T-moves approaches, while at the same time preserving desirable features…
This work proposes a fast iterative method for local steric Poisson--Boltzmann (PB) theories, in which the electrostatic potential is governed by the Poisson's equation and ionic concentrations satisfy equilibrium conditions. To present the…
A generalization of the standard model of Dirac particle in external electromagnetic field is proposed. In the generalization we take into account interactions of this particle with environment, which is described by the memory function.…
We compare exponential-type integrators for the numerical time-propagation of the equations of motion arising in the multi-configuration time-dependent Hartree-Fock method for the approximation of the high-dimensional multi-particle…
An algorithm for planning near time-optimal trajectories for systems with an oscillatory internal dynamics has been developed in previous work. It is based on assembling a complete trajectory from motion primitives called jerk segments,…
We establish new Harnack estimates that defy the waiting-time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal operators with bounded measurable coefficients. Moreover, we…
The outlook of a simple method to generate localized (soliton-like) potentials of time-dependent Schrodinger type equations is given. The conditions are discussed for the potentials to be real and nonsingular. For the derivative Schrodinger…
This paper describes an updated exponential Fourier based split-step method that can be applied to a greater class of partial differential equations than previous methods would allow. These equations arise in physics and engineering, a…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
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…
We establish error bounds of the Lie-Trotter splitting ($S_1$) and Strang splitting ($S_2$) for the Dirac equation in the nonrelativistic limit regime in the absence of external magnetic potentials, with a small parameter $0<\varepsilon\leq…
The method of moments in the context of Nonlinear Schrodinger Equations relies on defining a set of integral quantities, which characterize the solution of this partial differential equation and whose evolution can be obtained from a set of…