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…
Time-independent perturbation theory is an approximation scheme that applies in the following context: we know the solution to the eigenvalue problem of the Hamiltonian H 0, and we want the solution to H = H 0 +H 1 where H 1 is small compared to H 0 in a sense to be made precise ...
(t)\), where the time-independent generator\({\mathcal{L}}\)is an appropriate superoperator. To understand why this is so, we must compare the typical rate of change of\({\hat{\rho }}_{\rm{S}}(t)\)(given by\({\tau }_{{\rm{coh}}}^{-1}\)) with the ‘memory time’ ...
Real-time time-dependent density-functional theory (RT-TDDFT) and linear response time-dependent density-functional theory (LR-TDDFT) are two important approaches to simulate electronic spectra. However, the basis sets used in such calculations are usual
(SID) model”. Using the operator representation of indels and the technique of time-dependent perturbation theory, we express theab initioprobability as a summation over all alignment-consistent indel histories. Exploiting the equivalence relations between different indel histories, we find a “...
Between 1998 and 1999 the independent projects High-z Supernova Search Team and Supernova Cosmology Project showed results that the universe went through a late-time accelerated expansion phase [1,2]. This behavior has been confirmed by many independent observations [3,4,5], turning it into the...
The previous shift is nevertheless independent of the number of methyl groups (dimethylphenol, trimethylphenol) and of the nature of the predominant forms (thus of the pH value). Considering the close values of the shifts (with regard to phenol) of tributyl 4-methylphenol and of 4-cresol (4-...
If X and Y are independent exponential random variables with respective rates λ and μ, what is the conditional distribution of X given that X<Y? 9. Machine 1 is currently working. Machine 2 will be put in use at a time t from now. If the lifetime of machine i is exponential with...
Refs.2,39was based on a comparison of the potential energies of electronic ground and excited states of the four-atom complexes for a small set of geometries. Laser excitation rate coefficients were obtained as a phase-space averaged sum over excited states in time-independent perturbation theory...
What is more, for independent currents I1 and I2 it can very easily occur that I1 − I2 = 0 while I1 + I2 ≠ 0 at certain moments in time, leading to singular capacitances. We stress though, that this singularity is not a sign of a failure of the theory: ...