Wavefunction steady-state

Fig. 20 Charge carrier mobility in P3HT as a function of the charge carrier concentration. Squares refer to an experiment performed on a field effect transistor while circles refer to experiments done on an electrochemically doped sample. In the latter case the mobility is inferred from the steady state current at a given doping level. Solid and dashed lines have been fitted using the theory of [101]. The fit parameters are the site separation a, the prefactor Vq in the Miller-Abrahams-type hopping rate, the inverse wavefunction decay parameter y and the dielectric constant e. From [101] with permission. Copyright (2005) by the American Institute of Physics...

The influence of anisotropy of acceptor wavefunction upon tunnelling luminescence kinetics was treated in [104]. The conclusion was drawn that for the static tunnelling luminescence it just results in the redefinition of the (7o parameter. However, we are interested here in the non-steady-state kinetics and shall demonstrate below that, particularly at this stage, anisotropic recombination reveals distinctive behaviour which allows us to identify it. 

Using a plane wave representation for the electron wavefunction with 163 grid points and approximately 800 independent electronic and molecular configurations from the path integral molecular dynamics trajectories, we have also computed the density of states for the electron under different supercritical conditions of the solvents and the corresponding steady-state optical absorption spectra. The latter were computed within the dipolar approximation from the following expression within the Frank-Condon approximation ... 

Equation (14) defines the steady-state wavefunction of the DBA (or DA) system, 4 (t)) a cn(t) n)- Terms involving coefficients on the driving wire appear... 

In the quantum scattering approach the collision is modelled as a plane wave scattering off a force field which will in general not be isotropic. Incident and scattered waves interfere to give an overall steady state wavefunction from which bimolecular reaction cross-sections, cr, can be obtained. The characteristics of the incident wave are determined from the conditions of the collision and in general the reaction cross-section will be a function of the centre of mass collision velocity, u, and such internal quantum numbers that define the states of the colliding fragments, represented here as v and j. Once the reactive cross-sections are known the state specific rate coefficient, can be determined from. 

To be specific, Eq. (2.208) may be understood as the answer to the following question What is the steady state in a system in which a constant flux of particles, described by the incident wavefunction iAi(x) = Ae , impinges on the barrier from the left in region I This solution is given not by specifying quantum states and their energies (which is what is usually required for zero flux problems), but rather by finding the way in which the incident flux is distributed between different channels, in the present case the transmission and reflection channels. 

Heisenberg s uncertainty principle We can write Schrodinger s equation for a particle system that is not at steady state to describe the time-dependent wavefunction 4>(x, t) as follows ... 

The diabatic excited state population P2 shows rather regular oscillation for 4 times before becoming steadily decreasing after 300 fs. We note that the steady decrease in population beyond 300 fs is due to the wavefunction dissociating from the excited state (which is unphysical, see Sec. 5.4.1.1) and not from population transfer to the V surface. 

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