Taking into account the strong anisotropy of the nanostructure, one can use the adiabatic approximation
, in which fast transverse and slow in-plane movements may be considered separately, representing the electron wave function as follows:
The first approximation, which is called the adiabatic approximation
[5-7], assumes that the electronic wave functions adapt quasi-instantaneously to a variation of the nuclear configuration.
In this case, we can use adiabatic approximation
, which results in the following time-dependent perturbation for the electron Schrodinger equation [2, 5-8]:
and single electron approximation are usually used in the interaction between light and solid.
Considering that the height of the structure is very small comparing with the dimensions of the base, we can use the adiabatic approximation
where the 3D-confinement potential can be written as the sum between two potentials: the first one depending on the in-plane xy-dimensions and the second one depending on the z-dimension; that is, V([rho], z) = V1(p) + [V.sub.2] z; x,y), where the z-dependent confinement potential ([V.sub.2](z; x,y)) depends of the in-plane coordinates (x, y) (in this work this dependence is associated with the variations of the height of the QD).
The N-soliton interactions in the adiabatic approximation
for the MM (V (x) = 0) can be modelled by CTC .
For this particular approach, we used effective mass approximation and adiabatic approximation
The solution is proposed in terms of modes, propagating independently in the adiabatic approximation
, and described as a non-integer power series of a small parameter characterizing the stratified medium.
The authors use the Born-Oppenheimer adiabatic approximation
and show the parametric method for calculations for polyenes and acenes.
The time of flight was calculated for the proton and using the adiabatic approximation
. The yield and the logarithmic derivative of the yield with respect to a were calculated.
The maximum average current ([<j>.sub.max]) is reached, within this adiabatic approximation
, when the lower value of the resonance eigenbound state is equal to the incoming particle's energy, that is, for [OMEGA] = U - [([f.sub.0] + [DELTA]f).sup.2]/4, or [DELTA]f = 2K - [f.sub.0], for which case
This goal matches the needs of: (i) going beyond the simplest adiabatic approximation
-- commonly adopted in the description of ultrafast phenomena at the nanoscale; and(ii) dealing with the actual spatial inhomogeneities of many-electron systems at non-adiabatic level.