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After this maximum the ionization efficiency decreases in accord with the Saha-Langmuir-equation.
      
Using the Bethe-equation a numerical penetration depth-energy-relation for electrons was derived which gives good agreement with the experimental values.
      
Under suitable boundary conditions a method of integra ion is developed, which yields the exact solution of the relativistic three-particle-equation.
      
The conditions will be deduced for the exact solution of the Thomas-Fermi-equation for an atom or ion, which is deformed by non-spherical fields.
      
It is shown that the Dirac-equation can be solved for a superposition of Yukawapotentials by a modified perturbation procedure.
      
This transportmechanism is described by a Boltzmann-equation.
      
Master-equation for the statistical operator of solid state laser
      
The conditions for the existence of particular solutions are investigated for the space- and time-dependent linear Boltzmann-equation which describes the neutron field.
      
One can see immediately that the density of states,N(r, ω), at any positionr and high energiesω is always larger than the local BCS density of states if the space dependence of the order parameter is governed by the GL-equation.
      
By means of the Einstein-relation the coefficients in the Fokker-Planck-equation are related to the parameters in the phenomenological equations.
      
For the optical modelPerey andBuck did an exact nonlocal calculation with the Schr?dinger-equation in integro-differential form and also a good local approximation.
      
The nonlocal Schr?dinger-equation has been solved in the shell model case with a kernel-function, which is well known from optical model calculations.
      
This ionization and its dependence on temperature are in accord with the Saha-Langmuir-equation.
      
The well-known methods of Langevinequations and master-equation for a few discrete modes are generalized to meet also the case of a radiation field with continuous spectrum.
      
The ionization at higher temperatures and there the dependence on temperature are in agreement with the Saha-Langmuir-equation.
      
The relaxation of a strongly anisotropic two-component-plasma is treated by using the Balescu-Lenard-equation, i.e.
      
At higher temperatures there is a slight decrease ofΒ in the case of tungsten in agreement with the Saha-Langmuir-equation.
      
Bound-state solutions to the Bethe-Salpeter-equation of the Wick-Cutkosky model
      
A discussion of the Boltzmann-equation approach is also given.
      
By Taylor expansion one finds the time dependent Ginzburg-Landau-equation.
      
 

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