In this chapter, we discuss the time-discretization of time-dependent equations. Although the methods apply to general nonlinear time-dependent equations, their analysis is developed in the linear case and, more especially, for the advection-diffusion equation. First, we address the stability of ...
网络时薛丁格方程式 网络释义 1. 时薛丁格方程式 薛丁格方程式有多种表示方式,但主要分为含时薛丁格方程式(time dependent Schrodinger equation)与不含时薛丁格方程式(tim… case.ntu.edu.tw|基于 1 个网页
Time-dependent Hamiltonian dynamics can be formulated in evolution space independently of any inertial frame. The principle of geometric quantization extended to evolution space yields an intrinsic quantum theory equivalent to that based on the time-dependent Schrödinger equation. We restrict our attentio...
Real-time propagation (RTP) has become an appealing technique for the solution of the time-dependent Kohn–Sham calculations, namely, real-time time-dependent density-functional theory (RT-TDDFT), or general approximations to the time-dependent Schrödinger equation4,5,6,7,8,9. It is based ...
During the optimization process, the loads on the body are determined efficiently by solving the time-dependent, transonic small disturbance equation in two- dimensions. A novel contitiuous adjoint approach is then developed to obtain the sensitivities of a sample objective functional with respect to...
Equation (68) emphasizes that the shifted charge function can be taken to be time dependent, and we will assume that this time dependence is expressed as the time derivative of a fixed function f0(t). The solution for the electric field is thus of the form $${{{\bf{E}}}_{Q}^{\pr...
B. (1993) A stochastic differential equation with time-dependent and unbounded operator coefficients. J. Funct. Anal. 114: pp. 12-31B. R. Bhat and K. B. Sinha, "A stochastic differential equation with time-dependent and unbounded operator coefficients," J. Funct. Anal. 114 (1), 12-31...
The two meson equation has a closed solution leading to a single bound state for attractive renormalized coupling and a complete form for the scattering amplitude in the continuum. This form is easily adapted to the usual running coupling constant in the two meson energy. They also find that ...
Noting that the density is the diagonal of the one-body Green’s function in the equal-time limit, an exact integral expression for the time-dependent xc potential can be found through the Dyson equation for the interacting Green’s function when referred to the KS Green’s function209. Taki...
摘要: In this comment the authors use an invertible point transformation for the study of time-dependent equations derived from the equation R+C1Rn L=C2RmR=0. This procedure generalizes some results obtained recently by Leach and Gorringe (1990)....