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 ...
We reformulate the time-independent perturbation theory for quasinormal modes and express the corrections to the complex energy in terms of matrix elements. One main feature of the results is the appearance of an alternative definition for the norm, which is finite for quasinormal modes. Explicit ...
Using the adjoint system method, based on the mean-point second-order perturbation method, the first two probabilistic moments of time-independent sensitivity are formulated with means and cross-covariances of random design parameters as the input data. It enables one to obtain the second-order ...
(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 “...
|0 ↔ |1 ↔ |2 , this reduces to a single independent phase controlled by −(E01 − E00)t which then gives real entropy. 3.3 Two uncoupled oscillators We consider two uncoupled harmonic oscillators: the Hamil- tonian is H = En1n2 |n1, n2 n1, n2|, En1n2 = ω(n1 + n2 +...
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: ...
Time-dependent density functional theory continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics. Although in principle exact, the predictivity of the calculations is lim
This is achieved by pre-multiplying the drift matrix by the transformation matrix (\({{\varvec{D}}}{{\varvec{A}}}\)), which denotes that, if a variable is forced to remain constant, it’s rate of change is now independent of the other variables in the model. For the direct ...
performing numerically an ensemble overNmeasindependent trajectories or adding Gaussian noise to an ideal infinite ensemble (with standard deviation given by either Eq. (8) or (9)) will also be verified below. Short-term memory capacity In the previous sections, we have analytically assessed ...