No abstract

A pinning of the absorption edge of Cdl-,Mn,Te occurs for x > 0.4. Some authors have attributed this behaviour to a transition within the 3d5 localized levels of the Mn2+ ions. The possibility is analysed to observe such a transition in CdMnTe. A comparison with observations on spectra of various substitutional impurities of the 3d series on 11-VI crystals leads to the determination of an upper limit for the crystal field parameter Dq of the Mn atom in CdMnTe crystals and consequently to a lower limit for the energy difference between the ground and the first excited states in the d-shell of Mn. From a temperature and composition dependence recall of absorption and luminescence measurements previously performed, it is deduced that transitions between 3d5 levels of Mn2+ do not explain the anomalous behaviour of the absorption edge of CdMnTe for x > 0.4 and an alternative possible explanation is given.Ein Festsetzen der Absorptionskante von Cdl-,IvIn,Te tritt fur x > 0,4 auf. Einige Autoren ordnen dieses Verhalten einem Ubergang innerhalb der lokalisierten 3d5-Niveaus der Mn2+-Ionen zu. Die Moglichkeit der Beobachtung eines solchen ubergangs in CdMnTe wird analysiert. Ein Vergleich mit Beobachtungen an Spektren von verschiedenen Substitutionsverunreinigungen der 3d-Serien an 11-VI-Kristallen fuhrt zur Bestimmung einer oberen Grenze fur den Kristallfeldparameter Dq des Mn-Atoms im CdMnTe-Kristall und folglich zu einer unteren Grenzs fur die Energiedifferenz zwischen dem Grundzustand und dem ersten angeregten Zustand in der d-Schale des Mn. Aus der Temperatur-und Zusammensetzungsabhangigkeit von friiheren Absorptions-und Lumineszenzmessungen wird abgeleitet, daB ubergange zwischen den 3d5-Niveaus von MnZt das anomale Verhalten der Absorptionskante des CdMnTe fur x >0,4 nicht erklaren und es wird eine mogliche alternative ErklLrung vorgeschlagen.

By employing algebraic techniques we find the exact solutions of the Cauchy problem for two equations, which may be considered as n-dimensional generalization of the famous Fokker–Planck equation. Our approach is a combination of the disentangling techniques of R. Feynman with operational method developed in modern functional analysis in particular in the theory of partial differential equations. Our method may be considered as a generalization of the M. Suzuki method of solving the Fokker–Planck equation.

The exact solution of the Cauchy problem for a generalized "linear" vectorial Fokker-Planck equation is found using the disentangling techniques of R. Feynman and algebraic (operational) methods. This approach may be considered as a generalization of the Masuo Suzuki's method for solving the 1-dimensional linear Fokker-Planck equation.