Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.     

Eigenvalue problem for arbitrary linear combinations of a boson annihilation and creation operator

The eigenvalue problem for arbitrary linear combinations kα + μα^? of a boson annihilation operator α and a boson creation operator α^? is solved. It is shown that these operators possess nondegenerate eigenstates to arbitrary complex eigenvalues. The expansion of these eigenstates into the basic set of number states | n >, (n = 0, 1, 2, …), is found. The eigenstates are normalizable and are therefore states of a Hilbert space for | ζ | < 1 with ζ ? μ/k and represent in this case squeezed coherent states of minimal uncertainty product. They can be considered as states of a rigged Hilbert space for | ζ | ? 1. A completeness relation for these states is derived that generalizes the completeness relation for the coherent states | α 〉. Furthermore, it is shown that there exists a dual orthogonality in the entire set of these states and a connected dual completeness of the eigenstates on widely arbitrary paths over the complex plane of eigenvalues. This duality goes over into a selfduality of the eigenstates of the hermitian operators kα + k* α^? to real eigenvalues. The usually as nonexistent considered eigenstates of the boson creation operator α^? are obtained by a limiting procedure. They belong to the most singular case among the considered general class of eigenstates with ζ ? μ/k as a parameter.     

Sliding spark spectroscopy

Summary A new analytical radiation source combined with fiber optics linked to a diode array detection device with modified software is described. The direct-reading spectrometer simultaneously covers the wavelength range 185–510 nm with a spectral resolution of <1.5 nm. Intense optical emission is observed when positionally stable high-current surface sparks supplied by a pulse-generator with definite discharge parameters (max. 800 Ampere/pulse) are sliding over compact non-conductive materials such as plastics, glasses, quartz filters or powder pellets. Substrate vaporization, ionization and excitation processes in the surface discharge plasma channel generate emission corresponding to neutral and ionic states. The spectra are essentially composed of lines emitted by the electrode material (e.g. copper, silver), from the substrate under investigation, radiation continuum as well as structured background from the surrounding air atmosphere. Due to the occurrence of emission lines of reactive fillers, inorganic pigments and stabilizers, a rapid multi-element screening method is demonstrated. A rapid identification system (mix-up test) of PVC or fire-retardant thermoplastics within one second has been realized from the atomic emission line intensity originating from the sputtered copper electrode material according to its increased volatility in the presence of chlorine (modified Beilstein test).Puls-Plasma-Technik GmbH, Dortmund     

Bemerkungen zur Synthese von 3-Aminotoluol-5-sulfonsäure und 2-Aminotoluol-3-sulfonsäure

Some comments on the synthesis of 3-aminotoluene-5-sulfonic acid and 2-aminotoluene-3-sulfonic acid. Sulfonation of 3-nitrotoluene ( 5 ) yields predominantly the unsymetrical isomer 5-nitrotoluene-2-sulfonic acid ( 7 ), and lesser amounts of 5-nitrotoluene-3-sulfonic acid ( 6 ), previously reported as the major product. The desired 5-aminotoluene-3-sulfonic acid ( 3 ) was synthesized in preparative amounts from 6-aminotoluene-3-sulfonic acid (4) via the following sequence of reactions: diazotation and Sandmeyer replacement of 6-chlorotoluene-3-sulfonic acid ( 13 ), nitration of the sulfonyl chloride 14 under suitable conditions to give isomer free 6-chloro-5-nitrotoluene-3-sulfonyl chloride ( 15 ), hydrolysis to the sulfonic acid 16 and finally, simultaneous hydrogenolysis and reduction to 3 . The isomeric 7 was unequivocally prepared from 2-amino-5-nitrotoluene ( 9 ) via two routes: (1) diazotation, Sandmeyer thiocyanatation to 5-nitro-2-thiocyanatotoluene ( 10 ), Na₂S reduction to the di(2-methyl-4-nitro-phenyl)-disulfide ( 11 ), treatment with nitric acid and chlorine to give 5-nitrotoluene-2-sulfonyl chloride ( 12 ) and finally alkaline hydrolysis to 7 ; (2) Meerwein's SO₂ treatment of the diazonium salt derived from 9 leads directly to 12 and thence to 7 . 2-Aminotoluene-3-sulfonic acid ( 1 ) was prepared from the key intermediate 3-amino-2-nitrotoluene ( 18 ) via the same two routes used to prepare 7 from 9 . Both reaction sequences provided 2-nitrotoluene-3-sulfonly chloride, the hydrolysis product of which was reduced to 1 . Intermediate 18 was prepared in the following four steps from m-toluic acid ( 19 ): nitration to the 2-nitroderivative ( 20 ), whose acid chloride ( 21 ) was converted to 2-nitro-m-toluamide ( 22 ), and Hoffmann rearrangement to 18 .     

Ab initio studies on polymers. VI. Torsional potential in regular polyethylene chains

Ab initio crystal orbital calculations have been performed on regular polyethylene chains applying basis sets of minimal and double-zeta quality. Relative stabilities of periodic all-trans, all-gauche, and alternating trans–gauche conformers have been evaluated, including extensive geometry optimization. Potential curves for a simultaneous rotation around C? C single bonds from the all-trans to the all-gauche conformation have been computed applying the rigid-rotor approximation, the flexible-rotor approximation, and an additional reoptimization of C? C distances. A rigid-rotor potential curve from the all-trans to the alternating trans-gauche conformation has been computed as well. Results obtained are compared with ab initio calculations on butane and pentane and with semiempirical and empirical force-field studies on polyethylene.     

13C-NMR studies of marine natural products II. Total assignment of the 13C-NMR spectrum of asperdiol

¹³C-nmr spectral assignments for asperdiol are made with the aid of model compounds and T₁ relaxation behavior. Overall isotropic tumbling was inferred from the latter providing a supplemental means of multiplicity determination. Utilization of the T₁ relaxation times as an assignment criterion for select resonances in asperdiol is also described.