Volume 39, Issue 3

As previously shown, quantum physics for single pairs of creation and annihilation processes may be derived from first principles. Quantum physics at all can be therefore considered as an interplay of such elementary processes. This is easily possible if the number of pairs of processes is finite. Difficulties arise only for infinite numbers. The difficulties are similar to those occurring in the derivation of the equation for an oscillating string from that for an oscillator chain. It is true that the spectra of both systems are not continuously connected. However, a weaker theorem is more important: The chain eigenvalue of each order converges to the string one of the same order for an infinitely growing number of oscillators of a certain kind. Therefore both systems are continuously connected in the sense of semiconvergency. Exhausting the space continuum with a sequence of lattices equably becomming infinitely large and fine, the infinitely dimensional Hilbertspace is steadily connected with the finitely dimensional one in the sense of semiconvergency. It will be shown that the Hilbert spaces in the sequence of lattices yield the suitable tool for quantum physics as an interplay in the mentioned sense. This kind of Hilbert space, the so-called rational one, must be preferred in physics rather than the real one introduced by Hilbert, since all theories in physics are based on a finite number of data. In particular, we formulate Dirac's equation in the rational Hilbert space. It is shown that, even in quantum physics, a theorem of classical physics remains true, according to which relativity results from certain principles formulating most obvious experiences. We obtain the Lorentz invariant Dirac equation mainly from a modification of Newtons definition II according to which p = Hυ/c 2 (instead of p = m υ).

From comparison of simulated and experimental spectra in the nematic, smectic-A, and smectic-A phases of TBPrA it can be concluded that there are conformational changes of the molecule giving obviously rise to a continuous variation of the direction of the long molecular axis with respect to a frame of reference connected with a conformation of the molecule that was derived from the crystal conformation of TBBA.

The band structures of 11 one-dimensional (ID) poly-decker sandwich compounds with dif­ferent transition metal centers M (M = Mn, Fe, Co, Ni, Cu, Zn) and a variety of fivemembered π ligands L from the cyclopentadienyl moiety (C 5 H 5 ) to the pure boron ring B 5 H 5 have been studied by means of a semiempirical crystal orbital procedure based on the INDO approxima­tion in order to allow a priori predictions on possible semiconducting or conducting low-dimen­sional materials composed by ML fragments. To determine the (numerically) different self­energy corrections (i.e. long-range and short-range “correlations”) in the transition metal 3d spines and the ligand backbones approximate quasi-particle shifts have been employed for the correction of the Hartree-Fock (HF) band energies. The band structure properties (e.g., dispersion curves, density of states distributions, effective mass parameters, propagation times of charge carriers) are discussed in the light of the semiempirical tight-binding approach. It is shown that the forbidden band gaps are reduced with an increasing number of B atoms in the π ligands. The gap in the Mn(C 5 H 5 ) stack amounts to 8.27 eV, while overlapping dispersion curves are predicted in the Zn(B 5 H 5 ) derivative. This model polymer is the only intrinsic conductor in the series of the studied ID metallocenes; all other compounds require injected charge carriers (electrons or holes) in order to achieve partially filled bands. Injected holes in the Mn or Fe backbones lead to ID materials with conducting 3d spines; the charge transfer in this regime is best described as some type of hopping motion. The remaining poly-decker strands belong to the class of organic metals (injected carriers) with conductive pathways that are formed by diffuse ligand states leading to transfer processes that can be rationalized in terms of a band picture. The rotational profiles and the magnitudes of intracell and intercell interactions are also studied. The band structure properties (band gaps, characters of the valence and conduction bands) depend critically on the mutual orientations between neighbouring unit cells in the case of ligands with low spatial symmetries. General rules and strategies for synthetic approaches to organometallic ID materials containing 3d centers with small or vanishing band gaps are formulated.

The gravimetric method of interdiffusion measurement from a quartz frit is developped into an accurate general method. It is applied to a number of electrolyte solutions; for iodides and bromides a correction for the adsorption is applied. For the molten alkali nitrate systems (K-Cs)NO 3 at the molar fractions x Cs = 0.0 and x Cs = 0.1, (Na-Cs)NO 3 at x Cs = 0.0 and x Cs = 0.1. (Na-Rb)NO 3 , at x Rb = 0.0 and x Rb = 0.1 and (Na-K)NO 3 at ,x Na = 0.0, x Na = 0.3 and x Na = 1.0 the interdiffusion coefficient is determined over the temperature range of 600-723 K. The values obtained here are discussed in comparison to those from literature.

A static magnetic field parallel to the direction of propagation of an incident light beam causes a small shift in the value of the refractive index and, correspondingly, of the absorption coefficient of a chiral molecule. This shift is opposite for enantiomers. However, it occurs for arbitrarily polarized light and is therefore not a circular differential effect.

Thermally stimulated currents (TSC) in polyphenylene sulfide were measured in unpolarized and polarized samples. The TSC thermograms show a rapid increase in current at about 200 °C with an activation energy of about 1.6 eV. Additionally, in polarized samples a peak at about 150 °C related with the reorientational motions of the chain was found.

The molecular and electronic structure of 4H-pyran-4-one and its mono- and disubstituted sulfur analogues (1-4) are studied by the MNDO method. The salient structural features are qualitatively reproduced and the trend of changes of geometric parameters is in good agreement with experiment. The charge distributions exhibit strong polarization due to the large π-electron drift toward the exo-heteroatom. The protonated conjugated acids are considered too. It is found that exo-heteroatom protonation is favoured by 60-80 kcal/mol over the attachment of the proton to the intraring heteroatom. This is in accordance with experimental evidence. It is rationalized by the higher electron density centered on the exo-heteroatom and the appreciable increase in aromatic cyclic conjugation taking place upon the exo-protonation.

A graph-theoretical method for the calculation of the sextet polynomial is proposed. The method is easy and generally applicable. It is based on the construction of the Clar graph and on the calculation of its independence numbers.

Quasielastic Rayleigh scattering of 14.4 keV Mössbauer γ-radiation has been measured on 1,3-butanediol, yielding the width Γ of the central line (assumed to be Lorentzian) and its relative intensity, for momentum transfers corresponding to molecular dimensions (k = 0.9... 2.5 Å -1 ) at 243 K. Γ (k) rises fast and then saturates. An effective correlation time τ and jump width is derived characterizing the diffusional motion of individual molecules considered as entities. Fast motions (vibrations, librations) are taken into account explicitly. The correlation time τ compares well with results from other experiments. The temperature dependence was followed from 208 up to 263 K.

The nonlinear evolution of external ideal MHD-modes is determined from the equations of ideal MHD by employing a reductive perturbation method which uses a driving parameter for expansion. The reduction of the plasma equations is the same as for internal modes and was treated previously [1]. A main problem arising in addition for external modes is the reduction of the nonlinear boundary conditions. The set of reduced boundary conditions is obtained on the undisplaced boundary in the marginally stable equilibrium position. Another additional problem arises from the fact that the linear MHD operator is only selfadjoint for linear eigenmodes but not for the higher order mode corrections. This complicates the determination of nonlinear amplitude equations for the marginal mode which are obtained from solubility conditions. The amplitude equations are qualitatively the same as for internal modes. Quantitatively, the calculation of the coefficients in these is different. Explicit expressions for the coefficients are derived in full generality. The effect of higher order corrections to the nonlinear amplitude equations is discussed quantitatively for one of two possible cases and qualitatively for the other.