Self-adjoint extensions and spectral analysis in the Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential alpha x(-2). Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some `paradoxes` inherent in the `naive` quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.

UV optical absorption spectra analysis of beryl crystals from Brazil

The spectral decomposition analysis was applied to the optical absorption spectra of green and colorless beryl crystals from the Brazilian Eastern Pegmatitic province in the natural state, Submitted to heat treatment and irradiated with UV light The attributions of the lines were made taking into account highly accurate quantum mechanical calculations The deconvolution of the green beryl spectra revealed four lines, two of them around 12,000 cm(-1) (1 5eV) and two of them around 34,000 cm(-1) (4.2 eV) attributed to Fe(2+) and Fe(3+), respectively The deconvolution of the colorless beryl spectra without any treatment, after heating and for the same heat treatment followed by UV light irradiation revealed five lines The analysis of ratio relations showed that the lines at 36,400 cm(-1) (4.5 eV) and 41,400 cm(-1) (5 1 eV) belongs to a single defect attributed to a silicon dangling bond defect (=Si). Discussions and comparison with reported defects in quartz have supported the allocation of the lines at 61,000 cm(-1) (7.6 eV) and 43,800 cm(-1) (5 4 eV) to diamagnetic oxygen vacancy defect ( Si-Si ) and unrelaxed ( Si Si ) defect, respectively Finally, the line at 39.100 cm(-1) (4.8 eV), quite polarized along the c-axis, was attributed to a (Fe(2+) OH(-)) defect in the structural channels (C) 2009 Elsevier B V All rights reserved

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional non-relativistic motion of a particle in the potential field V(x) = g(1)x(-1) + g(2)x(-2), x is an element of R(+) = [0, infinity). For g(2) > 0 and g(1) < 0, the potential is known as the Kratzer potential V(K)(x) and is usually used to describe molecular energy and structure, interactions between different molecules and interactions between non-bonded atoms. We construct all self-adjoint Schrodinger operators with the potential V(x) and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying self-adjoint extensions by (asymptotic) self-adjoint boundary conditions. Solving spectral problems, we follow Krein`s method of guiding functionals. This work is a continuation of our previous works devoted to the Coulomb, Calogero and Aharonov-Bohm potentials.

Measurement of Rydberg state lifetimes using cold trapped neutral atoms

In this paper, I review some recent high-precision Rydberg state lifetime measurements using a cold-trapped sample of neutral atoms held in a magneto-optical trap. The measurements were performed in rubidium for the S, P and D states varying the principal quantum number from n = 26 to 45 using the field ionization technique. The experimental results were compared with quantum mechanical calculations and good agreement was observed. This is an important demonstration of how cold atomic samples can be used to perform high-precision spectroscopy in the time domain.

Study of the spectroscopic properties and first hyperpolarizabilities of disperse azo dyes derived from 2-amino-5-nitrothiazole

The solvatochromism and other spectroscopic and photophysical characteristics of four azo disperse dyes, derived from 2-amino-5-nitrothiazole, were evaluated and interpreted with the aid of experimental data and quantum mechanical calculations. For the non-substituted compound two conformers, E and Z, were proposed for the isolated molecules, being the second one considerably less stable. The optimization of these structures in combination with a SCRF methodology (IEFPCM, Simulating the molecules in a continuum dielectric with characteristics of methanol), suggests that the Z form is not stable in solution. This same behaviour is expected for the substituted compounds, which is corroborated by experimental data presented in previous investigations [A.E.H. Machado, L.M. Rodrigues, S. Gupta, A.M.F. Oliveira-Campos, A.M.S. Silva, J. Mol. Struct. 738 (2005) 239-245]. For the substituted compounds, two forms derived from E conformer (A and R) are possible. Quantum mechanical data suggest for the isolated molecules, that the low energy absorption hand of the E conformers involve at least two close electronic states. having the low-lying excited state a (1)(n,pi*) nature, and being the S-2 state attributed to a (1)(pi,pi*) transition. The data also suggest a small energy gap between the absorption peaks of A and B, related to the easy conversion between these forms. For the structures optimized in combination with the applied SCRF methodology, an states inversion is observed for the Substituted compounds, with a considerable diminish of the energy gap between A and B absorption peaks. The electronic spectra of these compounds are quite sensitive to changes in the solvent polarity. The positive solvatochromism is more evident in aprotic solvents, probably due to the polarization induced by the solute. These compounds do not fluoresce at 298 K, but present a small but perceptible fluorescence at 77 K, which seems to be favoured by the nature of the group in the 2 `-position of the phenyl ring. Moreover, such compounds present expressive values for first hyperpolarizability, which implies in good non-linear optics (NLO) responses and photoswitching capability. (C) 2008 Elsevier B.V. All rights reserved.

Effect of Different Solvent Ratios (Water/Ethylene Glycol) on the Growth Process of CaMoO(4) Crystals and Their Optical Properties

In this paper, calcium molybdate (CaMoO(4)) crystals (meso- and nanoscale) were synthesized by the coprecipitation method using different solvent volume ratios (water/ethylene glycol). Subsequently, the obtained suspensions were processed in microwave-assisted hydrothermal/solvothermal systems at 140 degrees C for 1 h. These meso- and nanocrystals processed were characterized by X-ray diffraction (X R I)), Fourier transform Raman (FT-Raman), Fourier transform infrared (FT-IR). ultraviolet visible (UV-vis) absorption spectroscopies, held-emission gun scanning electron microscopy (FEG-SEM). transmission electron microscopy (TEM). and photoluminescence (PL) measurements. X RI) patterns and FT-Raman spectra showed that these meso- and nanocrystals have a scheelite-type tetragonal structure without the presence of deleterious phases. FT-IR spectra exhibited a large absorption band situated at around 827 cm(-1), which is associated with the Mo-O anti-symmetric stretching vibrations into the [MoO(4)] clusters. FEG-SEM micrographs indicated that the ethylene glycol concentration in the aqueous solution plays an important role in the morphological evolution of CaMoO(4) crystals. High-resolution TEM micrographs demonstrated that the mesocrystals consist of several aggregated nanoparticles with electron diffraction patterns of monocrystal. In addition, the differences observed in the selected area electron diffraction patterns of CaMoO(4) crystals proved the coexistence of both nano- and mesostructures, First-principles quantum mechanical calculations based on the density functional theory at the B3LYP level were employed in order to understand the band structure find density of states For the CaMoO(4). UV-vis absorption measurements evidenced a variation in optical band gap values (from 3.42 to 3.72 cV) for the distinct morphologies. The blue and green PI. emissions observed in these crystals were ascribed to the intermediary energy levels arising from the distortions on the [MoO(4)] clusters clue to intrinsic defects in the lattice of anisotropic/isotropic crystals.

Study of the carbon dioxide chemical fixation-activation by guanidines

Fixation of CO(2) is one of the most important priorities of the scientific community dedicated to reduce global warming. In this work, we propose new methods for the fixation of CO2 using the guanidine bases tetramethylguanidine (TMG) and 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]-pyrimidine (TBD). In order to understand the reactions occurring during the CO(2) fixation and release processes, we employed several experimental methods, including solution and solid-state NMR, FTIR, and coupled TGA-FTIR. Quantum mechanical NMR calculations were also carried out. Based on the results obtained, we concluded that CO(2) fixation with both TMG and TBD guanidines is a kinetically reversible process, and the corresponding fixation products have proved to be useful as transcarboxylating compounds. Afterward, CO(2) thermal releasing from this fixation product with TBD was found to be an interesting process for CO(2) capture and isolation purposes. (C) 2008 Elsevier Ltd. All rights reserved.

Structural and Electronic Properties of Dipyridamole and Derivatives

Quantum mechanical calculations at the B3LYP theory level, together with the 6-31G* basis set, were employed to obtain the energy, ionization potential, and polarizabilites for dipyridamole and derivatives, which are compared with their biological activity. Density functional calculations of the spin densities were performed for radical formed by electron abstraction of dipyridamole and derivatives. The unpaired electron remains in dipyridamole is localized on the nitrogen atoms in the substituent positions 1, 3, 5, 7, 11, 12, 13, 14, with participation of the 9 and 10 carbons in the pyrimido-pyrimidine ring. The antioxidant activity is related with ionization potential, polarizability and Log P.