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showing 10 items of 6843 documents
Heisenberg Uncertainty Relation in Quantum Liouville Equation
2009
We consider the quantum Liouville equation and give a characterization of the solutions which satisfy the Heisenberg uncertainty relation. We analyze three cases. Initially we consider a particular solution of the quantum Liouville equation: the Wigner transformf(x,v,t) of a generic solutionψ(x;t) of the Schrödinger equation. We give a representation ofψ(x,t) by the Hermite functions. We show that the values of the variances ofxandvcalculated by using the Wigner functionf(x,v,t) coincide, respectively, with the variances of position operatorX^and conjugate momentum operatorP^obtained using the wave functionψ(x,t). Then we consider the Fourier transform of the density matrixρ(z,y,t) =ψ∗(z,t)…
Continuous-Variable Tomography of Solitary Electrons
2019
A method for characterising the wave-function of freely-propagating particles would provide a useful tool for developing quantum-information technologies with single electronic excitations. Previous continuous-variable quantum tomography techniques developed to analyse electronic excitations in the energy-time domain have been limited to energies close to the Fermi level. We show that a wide-band tomography of single-particle distributions is possible using energy-time filtering and that the Wigner representation of the mixed-state density matrix can be reconstructed for solitary electrons emitted by an on-demand single-electron source. These are highly localised distributions, isolated fro…
Fast evaluation of a linear number of local exchange matrices
2002
A fast method is described for evaluating multiple exchange matrices in a Gaussian atomic orbital basis. For insulators, it is asymptotically linear scaling, and is a generalization of the linear scaling exchange (LinK) method, which was formulated for a single exchange matrix [J. Chem. Phys. 109 (1998) 1663]. It is employed to evaluate exchange-type contractions of all derivative density matrices with two-electron integrals for a series of linear alkanes, linear polyacenes, and water clusters using STO-3G, 3-21G, and 6-31G* basis sets. Significant computational savings are obtained for molecules with as few as 10 non-hydrogen atoms.
Cu(II) and Cu(I) complexes with 1,2-dithiosquarate as a ligand; from molecular compounds to supramolecular network structures
2008
Abstract Four new complexes of copper(II) and/or copper(I) with 1,2-dtsq as a ligand have been synthesized and characterized by single crystal X-ray diffraction methods, [CuII(terpy)(1,2-dtsq)] (1), [CuII(dmen)(1,2-dtsq)]n (2), {[CuII(dmen)2][CuI(1,2-dtsq)]2}n·2nH2O(3) and {[CuII(men)2][CuI (1,2-dtsq)]2}n·nH2O (4) (1,2-dtsq = 1,2-dithiosquarate, dianion of 3,4-dimercapto-1-cyclobutene-1,2-dione; dmen = N,N-dimethylethylenediamine; men = N-methylethylenediamine, terpy = 2,2′:6,2″-terpyridine). Compound 1 consists of neutral [CuII(terpy)(1,2-dtsq)] mononuclear units which are held together by O⋯H–C and van der Waals interactions. Compound 2 is built of neutral [CuII(dmen)(1,2-dtsq)] entities …
Synthesis and characterization of a Cu(II) complex of 2-benzylmercapto-5- methyl-1,3,4-thiadiazole (C10H10N2S 2)
2008
A Cu(II) complex of 2-benzylmercapto-5-methyl-1,3,4-thiadiazole was synthesized and characterized. The crystal structure of the copper complex and the free ligand were determined by single-crystal X-ray diffraction at room temperature: {[Cu(C10H10N2S2) 2(Cl)2], P1 triclinic, a = 8.1450(2) Å, b = 8.1690(2) Å, c = 10.8180(3) Å, α = 97.4040(12)°, β = 101.6270(11)°, γ = 116.1431(14)°; C10H10N2S2 ligand, Pbca orthorhombic, a = 8.7938(7) Å, b = 9.6491(7) Å, c = 25.3552(18) Å}. The metal complex framework consists of discrete units that provide crystalline stability through a network of van der Waals contacts. The Cu(II) is coordinated by two chloride ions and two 2-benzylmercapto-5-methyl-1,3,4- …
Compositional and microhardness findings in tooth affected by X-linked hypophosphatemic rickets
2020
Background This study aimed to evaluate the X-linked hypophosphatemic rickets (XLHR)-related compositional and microhardness tooth aspects. Material and Methods One affected and one non-affected teeth by XLHR were sectioned transversely, and each section was separated for Micro-Raman spectroscopy, Knoop microhardness and scanning electron microscopy with energy dispersive x-ray microanalysis (SEM-EDS). The outcomes of these analyses were assessed. Results Outcomes of Raman analysis of inorganic/organic components (~958/~1250+~1450 cm−1) and carbonate/phosphate (~1070/~958 cm−1) ratios showed areas of altered enamel and dentin (interglobular dentin, calcospherites, and mantle dentin) with an…
Collisional Broadening of Rotational Lines in the Stimulated Raman Pentad Q-Branch of CD4
1992
Self- and argon-broadening coefficients are reported for a number of Raman Q-branch transitions in the nu(1) and nu(2) + nu(4) bands of (C-12)D4 at room temperature (296 K). The coefficients display a variation with j and with C exp n (symmetry species A, E, F) that is essentially independent of collision partner and which is similar to the j- and C exp n-dependence found in previous measurements of the IR line-broadening coefficients. The rotationally inelastic collision rates previously measured by Foy et al. (1988) for (C-13)D4 (V4 = 0, 1) in collision with (C-13)D4 or Ar account for only a part of the Raman broadening rate, suggesting possibly significant contributions to the linewidths…
Femtosecond coherent anti-Stokes Raman-scattering polarization beat spectroscopy of I2–Xe complex in solid krypton
2006
Time-resolved coherent anti-Stokes Raman-scattering (CARS) measurements are carried out to study the interaction between xenon atom and iodine molecule in a solid krypton matrix. Interference between the CARS polarizations of the "free" and complexed iodine molecules is observed, while the quantum beats of the complex are not detected due to low concentration. Vibrational analysis based on the polarization beats yields accurate molecular constants for the I2-Xe complex. The harmonic frequency of the I2-Xe complex is found to be redshifted by 0.90 cm-1 when compared to the free I2, whereas the anharmonicity is approximately the same. The dephasing rate of the complex is found to be somewhat …
First‐Derivative Fourier‐Transform Infrared Determination of Oxadiazon in Commercial Herbicide Formulations
2008
Abstract A Fourier‐transform infrared (FTIR) method has been developed for the quantification of oxadiazon in herbicide formulations. The method involves the extraction of the active ingredient by sonication of the samples with CHCl3 and direct measurement of the peak area values in first‐order derivate spectra from 1770 cm−1 to 1774 cm−1 corrected with a baseline point located at 1950 cm−1 and after a 5‐point smoothing. A limit of detection (3 s) of 0.03 mg g−1 and a typical relative standard deviation (RSD) of 1.3% were found. Results obtained were comparable with those found by liquid chromatography with UV detection. The proposed method involves a 7‐times reduction in solvent consumptio…
Determination of carbonates in waters by on-line vapor generation FTIR
1998
Abstract An electrically heated gas-permeation unit (GPU) has been employed for the vapor-generation Fourier transform infrared (FTIR) determination of total carbonate in waters. The developed method is based on the simultaneous injection of 100 μ l sample and 100 μ l nitric acid in a two-channel manifold with a merging zone, which provides the generation of CO 2 through the GPU, heated at 90°C, from which CO 2 is swept by a stream of N 2 to a long-path infrared gas cell. Absorbance measurements were made in the range from 2500 to 2150 cm −1 and the corresponding flow injection recordings were obtained as a function of time. The areas of these peaks are interpolated in a calibration equatio…