Comment on ``A new efficient method for calculating perturbative energies using functions which are not square integrable'': regularization and justification

The method recently proposed by Skala and Cizek for calculating perturbation energies in a strict sense is ambiguous because it is expressed as a ratio of two quantities which are separately divergent. Even though this ratio comes out finite and gives the correct perturbation energies, the calculational process must be regularized to be justified. We examine one possible method of regularization and show that the proposed method gives traditional quantum mechanics results.Comment: 6 pages in REVTeX, no figure

Operator Method for Nonperturbative Calculation of the Thermodynamic Values in Quantum Statistics. Diatomic Molecular Gas

Operator method and cumulant expansion are used for nonperturbative calculation of the partition function and the free energy in quantum statistics. It is shown for Boltzmann diatomic molecular gas with some model intermolecular potentials that the zeroth order approximation of the proposed method interpolates the thermodynamic values with rather good accuracy in the entire range of both the Hamiltonian parameters and temperature. The systematic procedure for calculation of the corrections to the zeroth order approximation is also considered.Comment: 22 pages, 7 Postscript figures, accepted for publication in Journal of Physics

Eigenvalue bounds for polynomial central potentials in d dimensions

If a single particle obeys non-relativistic QM in R^d and has the Hamiltonian H = - Delta + f(r), where f(r)=sum_{i = 1}^{k}a_ir^{q_i}, 2\leq q_i < q_{i+1}, a_i \geq 0$, then the eigenvalues E = E_{n\ell}^{(d)}(\lambda) are given approximately by the semi-classical expression E = \min_{r > 0}[\frac{1}{r^2} + \sum_{i = 1}^{k}a_i(P_ir)^{q_i}]. It is proved that this formula yields a lower bound if P_i = P_{n\ell}^{(d)}(q_1), an upper bound if$P_i = P_{n\ell}^{(d)}(q_k) and a general approximation formula if P_i = P_{n\ell}^{(d)}(q_i). For the quantum anharmonic oscillator f(r)=r^2+\lambda r^{2m},m=2,3,... in d dimension, for example, E = E_{n\ell}^{(d)}(\lambda) is determined by the algebraic expression \lambda={1\over \beta}({2\alpha(m-1)\over mE-\delta})^m({4\alpha \over (mE-\delta)}-{E\over (m-1)}) where \delta={\sqrt{E^2m^2-4\alpha(m^2-1)}} and \alpha, \beta are constants. An improved lower bound to the lowest eigenvalue in each angular-momentum subspace is also provided. A comparison with the recent results of Bhattacharya et al (Phys. Lett. A, 244 (1998) 9) and Dasgupta et al (J. Phys. A: Math. Theor., 40 (2007) 773) is discussed.Comment: 13 pages, no figure

Metal-support interaction and charge distribution in ceria-supported Au particles exposed to CO

Understanding how reaction conditions affect metal-support interactions in catalytic materials is one of the most challenging tasks in heterogeneous catalysis research. Metal nanoparticles and their supports often undergo changes in structure and oxidation state when exposed to reactants, hindering a straightforward understanding of the structure-activity relations using only ex situ or ultrahigh vacuum techniques. Overcoming these limitations, we explored the metal-support interaction between gold nanoparticles and ceria supports in ultrahigh vacuum and after exposure to CO. A combination of in situ methods (on powder and model Au/CeO2 samples) and theoretical calculations was applied to investigate the gold/ceria interface and its reactivity toward CO exposure. X-ray photoelectron spectroscopy measurements rationalized by first-principles calculations reveal a distinctly inhomogeneous charge distribution, with Au+ atoms in contact with the ceria substrate and neutral Au0 atoms at the surface of the Au nanoparticles. Exposure to CO partially reduces the ceria substrate, leading to electron transfer to the supported Au nanoparticles. Transferred electrons can delocalize among the neutral Au atoms of the particle or contribute to forming inert Auδ− atoms near oxygen vacancies at the ceria surface. This charge redistribution is consistent with the evolution of the vibrational frequencies of CO adsorbed on Au particles obtained using diffuse reflectance infrared Fourier transform spectroscopy

Contribution to understanding the mathematical structure of quantum mechanics

Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, commutation and uncertainty relations, probability density current, momentum operator, rules for including the scalar and vector potentials and antiparticles can be obtained from the probabilistic description of results of measurement of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrodinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the space-time Fisher information. The limit case of the delta-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many particle systems and the postulates of quantum mechanics are also discussed.Comment: 21 page

Multiply charged ions from iodine laser-produced plasma of medium- and high-Z targets

Maximum charge states of ions registered in the far expansion zone from laser-produced plasma of Al, Co, Ni, Cu, Ta, W, Pt, Au, Pb, and Bi are presented. The Thomson parabola spectrometer was used to display a general view of the ion species of an expanding plasma while detailed ion charge-energy spectra were determined by the cylindrical electrostatic ion energy analyzer. The current densities of highly charged ion groups above 20 mA/cm2 were measured by use of an ion collector at a distance of 1 m from the target. The photodissociation iodine laser system PERUN (λ = 1.315 μm, power density up to 1015 W cm−2) was employed as a drive

Ion production by lasers using high-power densities in a near infrared region

Results are presented of experiments on ion production from Ta targets using a short pulse (350-600 ps in focus) illumination with focal power densities exceeding 1014 Wcm-2 at the wavelength of an iodine photodissociation laser (1.315 μm) and its harmonics. Strong evidence of the existence of tantalum ions with the charge state +45 near the target surface was obtained by X-ray spectroscopy methods. The particle diagnostics point to the existence of frozen high charge states (4 MeV) for the highest observed charge states. A tentative theoretical explanation of the observed anomalous charge state freezing phenomenon in the expanding plasma produced by a subnanosecond laser pulse is give

Influence of 'Trichobilharzia regenti' (Digenea: Schistosomatidae) on the defence activity of 'Radix lagotis' (Lymnaeidae) haemocytes

Radix lagotis is an intermediate snail host of the nasal bird schistosome Trichobilharzia regenti. Changes in defence responses in infected snails that might be related to host-parasite compatibility are not known. This study therefore aimed to characterize R. lagotis haemocyte defence mechanisms and determine the extent to which they are modulated by T. regenti. Histological observations of R. lagotis infected with T. regenti revealed that early phases of infection were accompanied by haemocyte accumulation around the developing larvae 2–36 h post exposure (p.e.) to the parasite. At later time points, 44–92 h p.e., no haemocytes were observed around T. regenti. Additionally, microtubular aggregates likely corresponding to phagocytosed ciliary plates of T. regenti miracidia were observed within haemocytes by use of transmission electron microscopy. When the infection was in the patent phase, haemocyte phagocytic activity and hydrogen peroxide production were significantly reduced in infected R. lagotis when compared to uninfected counterparts, whereas haemocyte abundance increased in infected snails. At a molecular level, protein kinase C (PKC) and extracellular-signal regulated kinase (ERK) were found to play an important role in regulating these defence reactions in R. lagotis. Moreover, haemocytes from snails with patent infection displayed lower PKC and ERK activity in cell adhesion assays when compared to those from uninfected snails, which may therefore be related to the reduced defence activities of these cells. These data provide the first integrated insight into the immunobiology of R. lagotis and demonstrate modulation of haemocyte-mediated responses in patent T. regenti infected snails. Given that immunomodulation occurs during patency, interference of snail-host defence by T. regenti might be important for the sustained production and/or release of infective cercariae