Home About us Contact
|
Home About us Contact | ||
|
|
||
Quantum Mechanics (quantum + mechanic)
Selected AbstractsA probabilistic approach to quantum mechanics based on ,tomograms'FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7 2006M. Caponigro It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation of quantum states. This can be regarded as a classical-like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function and density operator. The relevant concepts of quantum mechanics are then reconsidered and the epistemological implications of such approach discussed. [source] Elementary Propositions and Essentially Incomplete Knowledge: A Framework for the Interpretation of Quantum MechanicsNOUS, Issue 1 2004William Demopoulos A central problem in the interpretation of non-relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper approaches the problem by presenting an analysis of the notion of an elementary physical proposition. The notion is shown to be realized in standard formulations of the theory and to illuminate the significance of proofs of the impossibility of hidden variable extensions. In the interpretation of quantum mechanics that emerges from this analysis, the philosophically distinctive features of the theory derive from the fact that it seeks to represent a reality of which complete knowledge is essentially unattainable. [source] Elementary Process Theory: a formal axiomatic system with a potential application as a foundational framework for physics supporting gravitational repulsion of matter and antimatterANNALEN DER PHYSIK, Issue 10 2010M.J.T.F. Cabbolet Abstract Theories of modern physics predict that antimatter having rest mass will be attracted by the earth's gravitational field, but the actual coupling of antimatter with gravitation has not been established experimentally. The purpose of the present research was to identify laws of physics that would govern the universe if antimatter having rest mass would be repúlsed by the earth's gravitational field. As a result, a formalized axiomatic system was developed together with interpretation rules for the terms of the language: the intention is that every theorem of the system yields a true statement about physical reality. Seven non-logical axioms of this axiomatic system form the Elementary Process Theory (EPT): this is then a scheme of elementary principles describing the dynamics of individual processes taking place at supersmall scale. It is demonstrated how gravitational repulsion functions in the universe of the EPT, and some observed particles and processes have been formalized in the framework of the EPT. Incompatibility of Quantum Mechanics (QM) and General Relativity (GR) with the EPT is proven mathematically; to demonstrate applicability to real world problems to which neither QM nor GR applies, the EPT has been applied to a theory of the Planck era of the universe. The main conclusions are that a completely formalized framework for physics has been developed supporting the existence of gravitational repulsion and that the present results give rise to a potentially progressive research program. [source] Austenitic Stainless Steels from Quantum Mechanical Calculations,ADVANCED ENGINEERING MATERIALS, Issue 4 2004L. Vitos Quantum mechanics is used to study the influence of the chemical composition on the elastic properties of austenitic stainless steels. Fe based alloys comprising approximately 15% Cr and 8% Ni are predicted to have the largest hardness among the usual austenitic steels, which, however, is associated with increased brittleness and susceptibility to various forms of localized corrosion. It is shown that few percent of additional Os or Ir to Fe15Cr8Ni alloy significantly improve on both of these shortcomings, without deteriorating the hardness. [source] A probabilistic approach to quantum mechanics based on ,tomograms'FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 7 2006M. Caponigro It is usually believed that a picture of Quantum Mechanics in terms of true probabilities cannot be given due to the uncertainty relations. Here we discuss a tomographic approach to quantum states that leads to a probability representation of quantum states. This can be regarded as a classical-like formulation of quantum mechanics which avoids the counterintuitive concepts of wave function and density operator. The relevant concepts of quantum mechanics are then reconsidered and the epistemological implications of such approach discussed. [source] Lie Theory for Quantum ControlGAMM - MITTEILUNGEN, Issue 1 2008G. Dirr Abstract One of the main theoretical challenges in quantum computing is the design of explicit schemes that enable one to effectively factorize a given final unitary operator into a product of basic unitary operators. As this is equivalent to a constructive controllability task on a Lie group of special unitary operators, one faces interesting classes of bilinear optimal control problems for which efficient numerical solution algorithms are sought for. In this paper we give a review on recent Lie-theoretical developments in finite-dimensional quantum control that play a key role for solving such factorization problems on a compact Lie group. After a brief introduction to basic terms and concepts from quantum mechanics, we address the fundamental control theoretic issues for bilinear control systems and survey standard techniques fromLie theory relevant for quantum control. Questions of controllability, accessibility and time optimal control of spin systems are in the center of our interest. Some remarks on computational aspects are included as well. The idea is to enable the potential reader to understand the problems in clear mathematical terms, to assess the current state of the art and get an overview on recent developments in quantum control-an emerging interdisciplinary field between physics, control and computation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] ,Erkenntnistheoretische Maschinen': Questions about the Sublime in the Work of Raoul SchrottGERMAN LIFE AND LETTERS, Issue 2 2002Karen Leeder This paper examines a new mode in recent German poetry. Far from the poetry influenced by the recent re-emergence of ,pop' culture, or the ,Alltagssprache' and ,simple Storys' of much recent writing from the former GDR, a number of poets have concerned themselves with modern science, particularly quantum mechanics and optics. These are among some of the most significant young poets of recent years (Thomas Kling, Franz Josef Czernin, Barbara Köhler, Durs Grünbein, Raoul Schrott etc.), figuring something which might be dubbed a contemporary of the ,poeta doctus'. This new discourse is interesting enough in itself, as poetry and science have, in the twentieth century at least, often been thought to be diametrically opposed. However, closer examination of this work, particularly that of Raoul Schrott (b. 1964), an ,emerging' and, paradoxically, already very distinguished writer, reveals that poetry and science can be understood as pro-foundly analogous; particularly in their use of metaphor. Fascinatingly, the contemporary discourse of science is set alongside classical (mythological) models in his work. They are both understood as finally hopeless projects to humanise the vast indifference of the universe: ,ein anderes sich in die leere/sagen'. The poem as ,epistemological machine' is set to interrogate the places where those human maps, models and vocabularies fail. The real territory of Schrott's work is thus revealed , in Hotels (1995), in essays, in four works of recent prose, and especially in Tropen (1998) , to be the boundaries of perception ,sub limes, where the models of human understanding fall away and point beyond themselves to an experience of the ,sublime'. [source] Geometrical properties of nodal surfaces of many-electron wave functionsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 10 2010Nikolai D. Chuvylkin Abstract Hypothesis of the exclusion of equipotential surfaces for many-electron wave functions (MWF) has been enunciated. This hypothesis clarifies the physical meaning of the Pauli exclusion principle and opens the way for future progress of new quantum-chemical methods for the construction of approximate MWFs differing from the traditional Hartree,Fock approximation. The equipotential surface exclusion principle has been tested on traditional representative "test systems" of quantum mechanics: the helium atom, the lithium atom, and the hydrogen molecule. Judging by the results of these tests, the use of the suggested approach can lead to a considerable increase in the efficiency of high-accuracy quantum-chemical calculations. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Degeneracy in one-dimensional quantum mechanics: A case studyINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 7 2010Adelio R. Matamala Abstract In this work we study the isotonic oscillator, V(x) = Ax2 + Bx,2, on the whole line ,, < x < + , as an example of a one-dimensional quantum system with energy level degeneracy. A symmetric double-well potential with a finite barrier is introduced to study the behavior of energy pattern between both limit: the harmonic oscillator (i.e., a system without degeneracy) and the isotonic oscillator (i.e., a system with degeneracy). © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010 [source] Gaussian approximation of exponential type orbitals based on B functionsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2009Didier Pinchon Abstract This work gives new, highly accurate optimized gaussian series expansions for the B functions used in molecular quantum mechanics. These functions are generally chosen because of their compact Fourier transform, following Shavitt. The inverse Laplace transform in the square root of the variable is used for Gauss quadrature in this work. Two procedures for obtaining accurate gaussian expansions have been compared for the required extended precision arithmetic. The first is based on Gaussian quadratures and the second on direct optimization. Both use the Maple computer algebra system. Numerical results are tabulated and compared with previous work. Special cases are found to agree before pushing the optimization technique further. The optimal gaussian expansions of B functions obtained in this work are available for reference. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] New perspectives on the fundamental theorem of density functional theoryINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2008Xiao-Yin Pan Abstract The fundamental theorem of time-independent/time-dependent density functional theory due to Hohenberg,Kohn (HK)/Runge,Gross (RG) proves the bijectivity between the density ,(r)/,(rt) and the Hamiltonian /(t) to within a constant C/function C(t), and wave function ,/, (t). The theorems are each proved for scalar external potential energy operators. By a unitary or equivalently a gauge transformation that preserves the density, we generalize the realm of validity of each theorem to Hamiltonians, which additionally include the momentum operator and a curl-free vector potential energy operator defined in terms of a gauge function , (R)/, (Rt). The original HK/RG theorems then each constitute a special case of this generalization. Thereby, a fourfold hierarchy of such theorems is established. As a consequence of the generalization, the wave function ,/, (t) is shown to be a functional of both the density ,(r)/,(rt), which is a gauge-invariant property, and a gauge function ,(R)/,(Rt). The functional dependence on the gauge function ensures that as required by quantum mechanics, the wave function written as a functional is gauge variant. The hierarchy and the dependence of the wave function functional on the gauge function thus enhance the significance of the phase factor in density functional theory in a manner similar to that of quantum mechanics. Various additional perspectives on the theorem are arrived at. These understandings also address past critiques of time-dependent theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Studies on some singular potentials in quantum mechanicsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2005Amlan K. RoyArticle first published online: 10 MAY 200 Abstract A simple methodology is suggested for the efficient calculation of certain central potentials having singularities. The generalized pseudospectral method used in this work facilitates nonuniform and optimal spatial discretization. Applications have been made to calculate the energies, densities, and expectation values for two singular potentials of physical interest, viz., (i) the harmonic potential plus inverse quartic and sextic perturbation and (ii) the Coulomb potential with a linear and quadratic term for a broad range of parameters. The first 10 states belonging to a maximum of ,, = 8 and 5 for (i) and (ii) have been computed with good accuracy and compared with the most accurate available literature data. The calculated results are in excellent agreement, especially in light of the difficulties encountered in these potentials. Some new states are reported here for the first time. This offers a general and efficient scheme for calculating these and other similar potentials of physical and mathematical interest in quantum mechanics accurately. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005 [source] Time asymmetry, nonexponential decay, and complex eigenvalues in the theory and computation of resonance statesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 2 2002Cleanthes A. Nicolaides Abstract Stationary-state quantum mechanics presents no difficulties in defining and computing discrete excited states because they obey the rules established in the properties of Hilbert space. However, when this idealization has to be abandoned to formulate a theory of excited states dissipating into a continuous spectrum, the problem acquires additional interest in many fields of physics. In this article, the theory of resonances in the continuous spectrum is formulated as a problem of decaying states, whose treatment can entail time-dependent as well as energy-dependent theories. The author focuses on certain formal and computational issues and discusses their application to polyelectronic atomic states. It is argued that crucial to the theory is the understanding and computation of a multiparticle localized wavepacket, ,0, at t = 0, having a real energy E0. Assuming this as the origin, without memory of the excitation process, the author discusses aspects of time-dependent dynamics, for t , 0 as well as for t , ,, and the possible significance of nonexponential decay in the understanding of timeasymmetry. Also discussed is the origin of the complex eigenvalue Schrödinger equation (CESE) satisfied by resonance states and the state-specific methodology for its solution. The complex eigenvalue drives the decay exponentially, with a rate ,, to a good approximation. It is connected to E0 via analytic continuation of the complex self-energy function, A(z), (z is complex), into the second Riemann sheet, or, via the imposition of outgoing wave boundary conditions on the stationary state Schrödinger equation satisfied by the Fano standing wave superposition in the vicinity of E0. If the nondecay amplitude, G(t), is evaluated by inserting the unit operator I = ,dE|E> Linking physiological mechanisms of coherent cellular behaviour with more general physical approaches towards the coherence of lifeIUBMB LIFE, Issue 11 2006Laurent Jaeken Abstract Schrödinger pointed out that one of the most fundamental properties of life is its coherent behaviour. This property has been approached from a physiological point of view by Ling in his 'association-induction hypothesis' and extended by Pollack (gel-sol theory), by Chaplin and by Kaivarainen (detailed studies of cellular water). The question of coherence has also been attacked from general physics in three independent approaches: from non-linear thermodynamics (Fröhlich), from quantum field theory (Del Giudice and his group) and from quantum mechanics (Davydov). In this paper all these approaches are unified. The emerging picture constitutes a new paradigm of life. iubmb Life, 58: 642 - 646, 2006 [source] A physiochemical theory on the applicability of soft mathematical models,experimentally interpretedJOURNAL OF CHEMOMETRICS, Issue 7-8 2010L. Munck Abstract An extension of chemometric theory was experimentally explored to explain the physiochemical basis of the very high efficiency of soft modelling of data from nature. Soft modelling in self-organisation was interpreted by studying the unique chemical patterns of mutants in an isogenic barley model on endosperm development. Extremely reproducible, differential Near Infrared (NIR) spectral patterns specifically overviewed the effect on cell composition of each mutant cause. Extended Canonical Variates Analysis (ECVA) classified spectra in wild type, starch and protein mutants. The spectra were interpreted by chemometric data analysis and by pattern inspection to morphological, genetic, molecular and chemical information. Deterministic chemical reactions were defined in the glucan pathway. A drastic mutation in a gene controlling the starch/ß-glucan composition changed water activity that introduced a diffusive, stochastic effect on the catalysis of all active enzymes. ,Decision making' in self-organisation is autonomous and performed by the soft modelling of the chemical deterministic and stochastic reactions in the endosperm cell as a whole. Uncertainty in the analysis of endosperm emergence was experimentally delimited as the ,indeterminacy' in local molecular path modelling ,bottom up' and the ,irreducibility' of the phenomenological NIR spectra ,top down'. The experiment confirmed Ilya Prigogine's interpretation of self-organisation by his dynamic computer model programmed with a self-modeled non-local extension of quantum mechanics (QM). The significance of self- organisation explained by Prigogine here interpreted as physiochemical soft modelling introduces a paradigm shift in macroscopic science that forwards a major argument for soft mathematical modelling and chemometrics to obtain full scientific legitimacy. Copyright © 2010 John Wiley & Sons, Ltd. [source] A theoretical study on the catalytic mechanism of Mus musculus adenosine deaminaseJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 12 2010Xian-Hui Wu Abstract The catalytic mechanism of Mus musculus adenosine deaminase (ADA) has been studied by quantum mechanics and two-layered ONIOM calculations. Our calculations show that the previously proposed mechanism, involving His238 as the general base to activate the Zn-bound water, has a high activation barrier of about 28 kcal/mol at the proposed rate-determining nucleophilic addition step, and the corresponding calculated kinetic isotope effects are significantly different from the recent experimental observations. We propose a revised mechanism based on calculations, in which Glu217 serves as the general base to abstract the proton of the Zn-bound water, and the protonated Glu217 then activates the substrate for the subsequent nucleophilic addition. The rate-determining step is the proton transfer from Zn-OH to 6-NH2 of the tetrahedral intermediate, in which His238 serves as a proton shuttle for the proton transfer. The calculated kinetic isotope effects agree well with the experimental data, and calculated activation energy is also consistent with the experimental reaction rate. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010 [source] Force-field parameters of the , and , around glycosidic bonds to oxygen and sulfur atomsJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 16 2009Minoru Saito Abstract The , and , torsion angles around glycosidic bonds in a glycoside chain are the most important determinants of the conformation of a glycoside chain. We determined force-field parameters for , and , torsion angles around a glycosidic bond bridged by a sulfur atom, as well as a bond bridged by an oxygen atom as a preparation for the next study, i.e., molecular dynamics free energy calculations for protein-sugar and protein-inhibitor complexes. First, we extracted the , or , torsion energy component from a quantum mechanics (QM) total energy by subtracting all the molecular mechanics (MM) force-field components except for the , or , torsion angle. The , and , energy components extracted (hereafter called "the remaining energy components") were calculated for simple sugar models and plotted as functions of the , and , angles. The remaining energy component curves of , and , were well represented by the torsion force-field functions consisting of four and three cosine functions, respectively. To confirm the reliability of the force-field parameters and to confirm its compatibility with other force-fields, we calculated adiabatic potential curves as functions of , and , for the model glycosides by adopting the , and , force-field parameters obtained and by energetically optimizing other degrees of freedom. The MM potential energy curves obtained for , and , well represented the QM adiabatic curves and also these curves' differences with regard to the glycosidic oxygen and sulfur atoms. Our , and , force-fields of glycosidic oxygen gave MM potential energy curves that more closely represented the respective QM curves than did those of the recently developed GLYCAM force-field. © 2009 Wiley Periodicals, Inc., J Comput Chem, 2009 [source] Electron correlation: The many-body problem at the heart of chemistryJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2007David P. Tew Abstract The physical interactions among electrons and nuclei, responsible for the chemistry of atoms and molecules, is well described by quantum mechanics and chemistry is therefore fully described by the solutions of the Schrödinger equation. In all but the simplest systems we must be content with approximate solutions, the principal difficulty being the treatment of the correlation between the motions of the many electrons, arising from their mutual repulsion. This article aims to provide a clear understanding of the physical concept of electron correlation and the modern methods used for its approximation. Using helium as a simple case study and beginning with an uncorrelated orbital picture of electronic motion, we first introduce Fermi correlation, arising from the symmetry requirements of the exact wave function, and then consider the Coulomb correlation arising from the mutual Coulomb repulsion between the electrons. Finally, we briefly discuss the general treatment of electron correlation in modern electronic-structure theory, focussing on the Hartree-Fock and coupled-cluster methods and addressing static and dynamical Coulomb correlation. © 2007 Wiley Periodicals, Inc. J Comput Chem 28: 1307,1320, 2007 [source] Tl(I)-the strongest structure-breaking metal ion in water?JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 6 2007A quantum mechanical/molecular mechanical simulation study Abstract Structural and dynamical properties of the Tl(I) ion in dilute aqueous solution have been investigated by ab initio quantum mechanics in combination with molecular mechanics. The first shell plus a part of the second shell were treated by quantum mechanics at Hartree-Fock level, the rest of the system was described by an ab initio constructed potential. The radial distribution functions indicate two different bond lengths (2.79 and 3.16 Å) in the first hydration shell, in good agreement with large-angle X-ray scattering and extended X-ray absorption fine structure spectroscopy results. The average first shell coordination number was found as 5.9, and several other structural parameters such as coordination number distributions, angular distribution functions, and tilt- and ,-angle distributions were evaluated. The ion,ligand vibration spectrum and reorientational times were obtained via velocity auto correlation functions. The TlO stretching force constant is very weak with 5.0 N m,1. During the simulation, numerous water exchange processes took place between first and second hydration shell and between second shell and bulk. The mean ligand residence times for the first and second shell were determined as 1.3 and 1.5 ps, respectively, indicating Tl(I) to be a typical "structure-breaker". The calculated hydration energy of ,84 ± 16 kcal mol,1 agrees well with the experimental value of ,81 kcal mol,1. All data obtained for structure and dynamics of hydrated Tl(I) characterize this ion as a very special case among all monovalent metal ions, being the most potent "structure-breaker", but at the same time forming a distinct second hydration shell and thus having a far-reaching influence on the solvent structure. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2007 [source] Fast fragments: The development of a parallel effective fragment potential methodJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 15 2004Heather M. Netzloff Abstract The Effective Fragment Potential (EFP) method for solvation decreases the cost of a fully quantum mechanical calculation by dividing a chemical system into an ab initio region that contains the solute plus some number of solvent molecules, if desired, and an "effective fragment" region that contains the remaining solvent molecules. Interactions introduced with this fragment region (for example, Coulomb and polarization interactions) are added as one-electron terms to the total system Hamiltonian. As larger systems and dynamics are just starting to be studied with the EFP method, more needs to be done to decrease the calculation time of the method. This article considers parallelization of both the EFP fragment-fragment and mixed quantum mechanics (QM)-EFP interaction energy and gradient computation within the GAMESS suite of programs. The iteratively self-consistent polarization term is treated with a new algorithm that makes use of nonblocking communication to obtain better scalability. Results show that reasonable speedup is achieved with a variety of sizes of water clusters and number of processors. © 2004 Wiley Periodicals, Inc. J Comput Chem 25: 1926,1935, 2004 [source] Characterization of asphaltene structure using atomic force microscopyJOURNAL OF MICROSCOPY, Issue 3 2008S. SABBAGHI Summary In this study, at the first stage, asphaltene was extracted. The roughness of asphaltene coating at different rpm was studied using an image analysis confocal microscopy. The basics of quantum mechanics and statistical thermodynamics are used to predict the potential energy and the intermolecular forces of asphaltene molecules. The functional forms for the potential energy and intermolecular forces are evaluated. Our final goal is to be able to observe and determine the surface structures of asphaltene micelles with scanning probe microscopes. So, the focus of the work on these unusual molecules is to characterize their structure, dynamics and thermodynamics and to establish the relationship between these properties and petroleum fluid behaviour. The existence of various nanostructures of asphaltene in petroleum has been extensively discussed. A set of fitted data is used to check the validity of the calculated results. The good agreement between the proposed models and the data is promising. [source] Density functional theory for chemical engineering: From capillarity to soft materialsAICHE JOURNAL, Issue 3 2006Jianzhong Wu Abstract Understanding the microscopic structure and macroscopic properties of condensed matter from a molecular perspective is important for both traditional and modern chemical engineering. A cornerstone of such understanding is provided by statistical mechanics, which bridges the gap between molecular events and the structural and physiochemical properties of macro- and mesoscopic systems. With ever-increasing computer power, molecular simulations and ab initio quantum mechanics are promising to provide a nearly exact route to accomplishing the full potential of statistical mechanics. However, in light of their versatility for solving problems involving multiple length and timescales that are yet unreachable by direct simulations, phenomenological and semiempirical methods remain relevant for chemical engineering applications in the foreseeable future. Classical density functional theory offers a compromise: on the one hand, it is able to retain the theoretical rigor of statistical mechanics and, on the other hand, similar to a phenomenological method, it demands only modest computational cost for modeling the properties of uniform and inhomogeneous systems. Recent advances are summarized of classical density functional theory with emphasis on applications to quantitative modeling of the phase and interfacial behavior of condensed fluids and soft materials, including colloids, polymer solutions, nanocomposites, liquid crystals, and biological systems. Attention is also given to some potential applications of density functional theory to material fabrications and biomolecular engineering. © 2005 American Institute of Chemical Engineers AIChE J, 2006 [source] Structural and vibrational study of 2-(2,- furyl)-4,5-1H -dihydroimidazoleJOURNAL OF PHYSICAL ORGANIC CHEMISTRY, Issue 12 2009Juan Zinczuk Abstract In this study 2-(2,-furyl)-4,5-1H -dihydroimidazole (1) was prepared and then characterized by infrared, Raman, and multidimensional nuclear magnetic resonance (NMR) spectroscopies. The crystal and molecular structures of 1 were determined by X-ray diffraction methods. The density functional theory (DFT) and second-order Møller,Plesset theory (MP2) with Pople's basis set show that there are two conformers for the title molecule that have been theoretically determined in the gas phase, and that only one of them, conformer I, is present in the solid phase. NMR spectra observed for 1 were successfully compared with the calculated chemical shifts at the B3LYP/6-311++G** level theorized for this conformer. The harmonic vibrational frequencies for the optimized geometry of the latter conformer were calculated at the B3LYP/6-311++G** level in the approximation of the isolated molecule. For a complete assignment of the IR and Raman spectra in the solid phase of 1, DFT calculations were combined with Pulay´s scaled quantum mechanics force field (SQMFF) methodology to fit the theoretical frequency values to the experimental ones. Copyright © 2009 John Wiley & Sons, Ltd. [source] The Krein,von Neumann extension and its connection to an abstract buckling problemMATHEMATISCHE NACHRICHTEN, Issue 2 2010Mark S. Ashbaugh Abstract We prove the unitary equivalence of the inverse of the Krein,von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, S , ,IH for some , > 0 in a Hilbert space H to an abstract buckling problem operator. In the concrete case where in L2(,; dnx) for , , ,n an open, bounded (and sufficiently regular) domain, this recovers, as a particular case of a general result due to G. Grubb, that the eigenvalue problem for the Krein Laplacian SK (i.e., the Krein,von Neumann extension of S), SKv = ,v, , , 0, is in one-to-one correspondence with the problem of the buckling of a clamped plate, (-,)2u = , (-,)u in ,, , , 0, u , H02(,), where u and v are related via the pair of formulas u = SF -1 (-,)v, v = , -1(-,)u, with SF the Friedrichs extension of S. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.) (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Elementary Propositions and Essentially Incomplete Knowledge: A Framework for the Interpretation of Quantum MechanicsNOUS, Issue 1 2004William Demopoulos A central problem in the interpretation of non-relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper approaches the problem by presenting an analysis of the notion of an elementary physical proposition. The notion is shown to be realized in standard formulations of the theory and to illuminate the significance of proofs of the impossibility of hidden variable extensions. In the interpretation of quantum mechanics that emerges from this analysis, the philosophically distinctive features of the theory derive from the fact that it seeks to represent a reality of which complete knowledge is essentially unattainable. [source] Thomas Pynchon: Gravity's Rainbow.ORBIS LITERARUM, Issue 3 2009The Ideas of the Opposite Thomas Pynchon's highly complex novel deals with the personal and social difficulty of accepting a new worldview. Set at the end of World War II and in its aftermath, the protagonists find themselves at the crossroads between Newtonian mechanics, epitomized by the V2 rockets, and the foreshadowed atom bomb, which is based on the theory of relativity and quantum mechanics. The style of Gravity's Rainbow resembles the scene of a subatomic world: it is presented as an ever-changing kaleidoscope of characters, places, events and interactions, which are constantly redetermined in relation to each other in an unpredictable manner. Pynchon manages to create a unifying theme by making all the twists in the plot comprehensible as manifestations of the underlying attempt to reconstruct selfhood. In addition, he refers recurrently to the motif of light, both as a physical entity at the center of modern physics and as a literary symbol of classical stability. In the end, his main protagonist himself turns into a mysterious source of light. [source] A Fourier optics approach to the dynamical theory of X-ray diffraction , continuously deformed crystalsACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2004Giovanni Mana X-ray diffraction in continuously deformed crystals is considered by application of Fourier optics and from the viewpoint of the analogy between X-ray dynamics and the motion of two-level systems in quantum mechanics. Different forms of Takagi's equations are traced back to a common framework and it is shown that they are different ways to represent the same propagation equation. A novel way to solve Takagi's equations in the presence of a constant strain gradient is presented and approximation methods derived from quantum mechanics are considered. Crystal deformation in X-ray interferometry and two-crystal spectrometry are discussed and it is demonstrated that Si lattice-parameter measurements depend on the diffracting plane spacing on the crystal surface. [source] Probabilistic observables, conditional correlations, and quantum physicsANNALEN DER PHYSIK, Issue 7 2010C. Wetterich Abstract We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated subsystem. The "coarse graining of the information" to micro-states implies probabilistic observables. For two-level probabilistic observables only a probability for finding the values one or minus one can be given for any micro-state, while such observables could be realized as classical observables with sharp values on a substate level. For a continuous family of micro-states parameterized by a sphere all the quantum mechanical laws for a two-state system follow under the assumption that the purity of the ensemble is conserved by the time evolution. The correlation functions of quantum mechanics correspond to the use of conditional correlation functions in classical statistics. We further discuss the classical statistical realization of entanglement within a system corresponding to four-state quantum mechanics. We conclude that quantum mechanics can be derived from a classical statistical setting with infinitely many micro-states. [source] Hidden nonassociative structure in supersymmetric quantum mechanicsANNALEN DER PHYSIK, Issue 6 2010V. Dzhunushaliev Abstract It is shown that the Hamilton equations in supersymmetric quantum mechanics can be presented in nonassociative form, where the Hamiltonian is decomposed into two nonassociative factors. [source] Intrinsic decoherence in the interaction of two fields with a two-level atomANNALEN DER PHYSIK, Issue 6 2009R. Juárez-Amaro Abstract We study the interaction of a two-level atom and two fields, one of them classical. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to neglect some terms in the rotated Hamiltonian. Then we solve a variation of the Schrödinger equation that models decoherence as the system evolves through intrinsic mechanisms beyond conventional quantum mechanics rather than dissipative interaction with an environment. [source]
| | ||||||||||||||||||||||||