Volume 53, Issue 8

Quantum mechanics is spectacularly successful on the technical level but the meaning of its rules remains shrouded in mystery even more than seventy years after its inception. Quantum-mechanical probabilities are often considered as fundamentally different from classical probabilities, in disre-gard of the work of Cox (1946) -and of Schrödinger (1947) -on the foundations of probability theory. One central question concerns the superposition principle, i. e. the need to work with inter-fering wave functions, the absolute squares of which are probabilities. Other questions concern the relationship between spin and statistics or the collapse of the wave function when new data become available. These questions are reconsidered from the Bayesian point of view. The superposition principle is found to be a consequence of an apparently little-loiown mathematical theorem for non-negative Fourier polynomials published by Fejer in 1915 that implies wave-mechanical inter-ference already for classical probabilities. Combined with the classical Hamiltonian equations for free and accelerated motion, gauge invariance and particle indistinguishability, it yields all basic quantum features -wave-particle duality, operator calculus, uncertainty relations, Schrödinger equation, CPT invariance and even the spin-statistics relationship -which demystifies quantum mechanics to quite some extent.

Molecular dynamics simulations of molten DyCl 3- NaCl were carried out at liquidus temperatures of the phase diagram. The chemical potential and the activity of NaCl was successfully estimated with the method proposed by Powles et al., which requires only positional data of the ions at the temperatures in question.

If the observed superluminal quantum correlations are disturbed by turbulent fluctuations of the ze-ro point vacuum energy field, with the turbulent energy spectrum assumed to obey the universal Kol-mogoroff law, a length is derived above which the correlations are conjectured to break. A directional dependence of this length would establish a preferred reference system at rest with the zero point ener-gy. Assuming that the degree of turbulence is given by the small anisotropy of the cosmic microwave background radiation, a length of ~60 km is derived above which the correlations would break.

Beams of clusters, the latter containing about 10 6 nitrogen molecules, were reflected by polished metal surfaces, and the direction, the velocity and the composition of the reflected beams were studied as functions of the direction of the incident beam. It turned out that the clusters leave the reflector surface almost tangentially, with reduced velocity, and that besides the clusters the beams contain gaseous nitrogen formed during the impact.

The analysis of the high resolution FT-IR spectra of the perpendicular bands v 7 (E') at about 1550 cm -1 and V 9 (E') at about 1170 cm -1 of the isotopomers 12 C 3 14 N 3 H 3 , 13 C3 14 N 3 H 3 , and l2 C 3 I5 N 3 H 3 is given. Both bands proved to be free from accidental resonances. The molecular constants of the state v 7 = 1 and v 9 = 1 of the isotopomers under consideration are listed. The weak difference band v 9 -v l4 (E" → E') of 12 C 3 14 N 3 H 3 was recorded and analyzed, using the molecular constants of v 9 = 1 [this work] and V 14 = 1 [of 1995], This analysis proves the quality of the molecular constants of the fundamental v 14 which is IR-inactive.

This paper deals with the morphology and surface chemistry of faceted voids existing in singlequasicrystalline icosahedral Al 70.5 Pd 21.0 Mn 8.5 . By observation with a scanning electron microscope of surfaces obtained by cleavage of the quasicrystal, the habit planes of the dodecahedral voids were identified. The chemical surface composition of the void surface was determined by Auger electron spectroscopy after cleavage in ultra-high vacuum.

The excited state dipole moments of some benzamide derivatives are determined. The method of solvent induced shifts of electronic absorption bands in comparison with their positions in the gas phase is used. Some regular trends revealed in the obtained data are discussed. The present results are compared with those available in the literature.

Using the extended Painlevé analysis, we obtained some higher dimensional integrable models with the Painlevé property from the (1+1)-dimensional Schwarz KdV equation.

Magnetic measurements were carried out on different samples of Lithium-Manganese spinel LiMn 2 O 4 , great care having been taken to avoid the presence of spurious magnetic phases, such as Mn 3 O 4 . Susceptibility data, showing deviations from paramagnetic behaviour at about 40 K, were analyzed in terms of local magnetic interactions, taking into account the structural and transport properties of these com-pounds. The magnetic response of pure and stoichiometric samples suggests that the onset of a longrange magnetic ordering is hindered by the topological frustration of the antiferromagnetic octahedral sublattice of the spinel.

The regular-hexagon-shaped benzenoid hydrocarbons: B 1 = benzene (C 6 H 6 ), B 2 = coronene (C 24 H 12 ), B 3 = circumcoronene (C 54 H 18 ), B 4 = circumcircumcoronene (C 150 H 30 ), etc. possess unique topological properties. General expressions for the most important of such properties (number of fun-damental structural invariants, number of Kekule and Clar structures, number of aromatic sextets, Wiener and Szeged indices, spectral moments) are given, including a number of results that are communicated here for the first time. Cyclic conjugation in circumcoronenes is analyzed by means of its energy-effect, and found to agree with the predictions of Clar's aromatic sextet theory only in the case of B 1 and B 2 .

The absolute configuration of bis(tetrahydropyran-2-yl)methane (1) was determined by comparison of measured and calculated CD spectra. The theoretical CD spectra were obtained by means of the CNDO/2S method. The five presumably lowest local minima on the energy hypersurface of the title compound were used to describe the conformer equilibrium mixture. The geometries of these conformers were calculated employing the MM3 force field, the semiempirical AM1 method and one-determinant ab initio calculations employing the 6-31G* basis set. Boltzmann factors were then obtained using relative energies calculated with three different basis sets and including correlation- and zero point vibrational energy. Based on the sign of the observed and calculated longest wavelength Cotton effect we assign an absolute configuration to the compound which is in keeping with the chirality expected from the assumed reaction mechanism. The results of force field and ab initio calculations converge to the point that the conformer equilibrium is dominated (85 -96%) by one single conformer which is energetically separated from the other conformers by about 2-3 kcal/mol. This result agrees with previous experimental data.

The fluorescence lifetimes of 4-cyano-N,N-dimethylaniline (CDMA), measured in propylene glycol at 293 K using frequency-domain fluorometry, in the short emission (SE) and long emission (LE) bands are 20 ps and 1.65 ns, respectively. The higher emission anisotropies in the SE band compared to that in the LE band are due to weaker rotational depolarization of fluorescence. Emission anisotropy decays imply that the initial limiting emission anisotropy, r (0), is the same in the SE and LE bands and amounts to 0.28. This reflects the fact that the directions of transition moments in these bands are parallel. In the case of CDMA in propylene and ethylene glycol at temperatures from 293 to 343 K, viscosity more strongly affects the relaxation to the TICT state than does the change in polarity of the solvents used.

The phase I of [H 3 N(CH 2 ) 3 NH 3 ]CdI 4 • 2H 2 O (1) crystallizes with isolated [CdI 4 ] 2- tetrahedra; monoclinic, C2/c, Z = 8, a = 1702.6(3), b= 1459.3(3), c= 1555.5(3) pm, and ß= 120.32(3)° at 299 K. (1) shows a first-order phase transition at T 1↔II = 245 K. The eight 127I (v 1 ) NQR lines in phase II change discontinuously into four lines in phase I. The transition entropy from DSC measurements, ∆S = 5.0 J K 1- mol -1 , shows that this transition is probably due to order-disorder of cations. [H 3 CNH 2 (CH 2 ) 3 NH 3 ]CdBr 4 (2) crystallizes with isolated [CdBr 4 ] 2- tetrahedra; orthorhombic P2 1 2 1 2 1 , Z = 4,a= 1447.8(5), b = 1280.3 (4), c = 709.7(3) pm at 299 K. (2) shows four 81 Br NQR lines between II and around 325 K, above which temperature the lines disappear. [(CH 3 ) 4 N] 2 CdBr 4 (3) shows a second-order phase transition at T 1↔II = 271 K. Three of four 81 Br NQR lines in phase II disappear below this transition point, the other line can be observed up to 315 K. The transition entropy, ∆S = 9.01 J KT -1 mol -1 , indicates that the transition is an order-disorder type of the cations. [(CH 3 ) 3 S] 2 CdBr 4 (4) shows a first-order type phase transition at T 1↔II = 304 K. The four lines spectrum of 81 Br NQR is observed in phase II and disappears above the transition point. The transition entropy, ∆S = 46.8 J K - 1 mol -1 is abnormally large. The role of the hydrogen bond and the bridging power between the halogen and cadmium atoms upon the formation of the condensed anion structure is discussed.

Diode laser spectra of the rare gas - spherical top van der Waals complexes Ar-CH 4 and Kr-CH 4 were measured in the wavelength region near 1310 cm -1 and assigned. The most prominent lines of both complexes exhibit three dense but well resolved R P 0 , Q R 0 , and R Q 0 branches, correlated to the R(0) transition of the triply degenerate bending vibration v 4 of methane, CH 4 . A model Hamiltonian based on Coriolis coupled states was applied for the assignment, analysis and fitting of the spectra to within the experimental accuracy of ≈ 15 MHz. The rotational B constants of the upper and lower states determined from the three allowed branches appeared to be strongly correlated. The precision in the determination of the rotational B constants of the two complexes was substantially increased by additional recording of several weak transitions in the nearly forbidden Q P 0 and R R 0 branches, which were fitted together with the allowed transitions. The separation between the rare gas atom and the methane molecule in the ground vibrational state was determined to be 3.999 Å and 4.094 Å for Ar-CH 4 and Kr-CH 4 , respectively. The measured small values of the splitting between the K=0 and the K = ±1 levels in the vibrationally excited state (0.39 cm -1 and 0.67 cm -1 for Ar-CH 4 and Kr-CH 4 , respectively), which characterizes the anisotropy of the intermolecular potential, indicated that Kr-CH 4 and Ar-CH 4 together with Ne-SiH 4 represent examples close to the free rotor limit, where the spherical top CH 4 is almost free to rotate within the complex. In comparison, the previously analyzed Ar-SiH 4 van der Waals molecule is closer to the hindered rotor limit.