现在回忆一下前面 (4) 式 i\hbar{\partial\hat U(t,t_0)\over\partial t}=\hat H\hat U(t,t_0) ,现在我们把相互作用绘景下的时间演化算符代入并计算 \begin{align} i\hbar{\partial\hat U_0(t,t_0)\hat U_\mathcal I(t,t_0)\over\partial t}&=\hat H\hat U_0(t,t_0)\hat U_...
一、不含时微扰论(非简并)在量子力学中我们学到了一些基本模型,比如谐振子、氢原子。对于这些基本模型,我们能直接解出系统的本征态和能级。而实际系统不可避免地会被外界干扰,这时系统的哈密顿量往往不再是可…
Perturbation Theory General Analysis Dirac Perturbation TheoryExample withH1(t)Inelastic Cross Section Example withH1(t) Inelastic Cross Section H1Independent of TimeParticle in Continuum in Final StateRelation to Previous Scattering TheoryScattering of Charged Lepton from Atom Particle in Continuum in ...
The effects of the periodical time-dependent perturbation on a KdV (Korteweg de Vries) soliton are studied. Expanding the perturbation term into a Fourier series, we find that the time-independent term will lead to th...
Second-Order Time-Dependent Perturbation Theory Let us consider the extension of time-dependent perturbation theory to second order in the interaction H 1 (t). The starting point is the set of differential equations i¯ h da (j+1) n (t) dt = m n|H 1 (t)|m e iωnmt a (j)...
We develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. We focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles. At a critical value of the destruction rate there is a continuous phase transition between...
The time-dependent quantum perturbation theory developed by Born, Heisenberg and Jordan in 1926 is revisited. We show that it not only reproduces the standard theory formulated in the interaction picture, but also allows one to construct more accurate approximations if time averaging techniques are ...
Perturbation theoryWe describe radiative processes in Quantum Cosmology, from the solutions of the Wheeler De Witt equation. By virtue of this constraint equation, the quantum propagation of gravity is modified by the matter interaction hamiltonian at the level of amplitudes. In this we generalize ...
A simple perturbation theory is proposed for single molecule orientational time correlation functions Cl,m(t). These functions are obtained by approximating the corresponding memory functions Kl,m(t) by the product of the free rotor memory function times a gaussian decay involving the mean square ...
Let us consider the extension of time-dependent perturbation theory to second order in the interaction H 1 (t). The starting point is the set of differential equations i h da (j+1) n (t) dt = m n|H 1 (t)|me iωnmt a (j) m (t), j = 0, 1, 2,. .. (1) If we assu...