Quantum mechanics interpretation

The quantum mechanics interpretation of these observations is that the initial state of the drum head is a superposition of eigenstates ... 

We use an example to illustrate the importance of two operators commuting to quantum mechanics interpretation of experiments. Assume that an experiment has been... 

Other approximate, more empirical methods are the extended Huckel 31> and hybrid-based Hiickel 32. 3> approaches. In these methods the electron repulsion is not taken into account explicitly. These are extensions of the early Huckel molecular orbitals 4> which have successfully been used in the n electron system of planar molecules. On account of the simplest feature of calculation, the Hiickel method has made possible the first quantum mechanical interpretation of the classical electronic theory of organic chemistry and has given a reasonable explanation for the chemical reactivity of sizable conjugated molecules. 

The fundamental quantum-mechanical interpretation by Ramsey of the NMR parameters of chemical shift [123, 124] and spin-spin J coupling [125, 126] still forms the basis of our understanding of these terms, as has been recently noted [127]. However, Ramsey neglected relativistic effects, which are very significant for the heavier nuclei such as 199Hg, 207Pb, and 203 205xi [127]. Derivations and discussion of Ramsey s theoretical results are found in the textbook by Slichter [26]... 

Quantum-Mechanical Interpretation of Nuclear Quad-rupole Coupling Data (Scrocco). 

Ralph Fowler, "A Report on Homopolar Valency and Its Quantum-Mechanical Interpretation," 26246, in Chemistry at the Centenary (1931) Meeting of the British Association for the Advancement of Science (Cambridge W. Heffer and Sons, 1932) 226. 

Coulson s generation of quantum theoretical chemists was struck by the fact that the mathematical physics of wave mechanics did not result in fundamental breakthroughs or discoveries in chemistry. As we have seen, Mulliken claimed that his initial work in quantum mechanics "interpreted," rather than "discovered," chemical facts. Alberte Pullman commented in 1970 ... 

A quantum-mechanical interpretation of Miedema s parameters has already been proposed by Chelikowsky and Phillips (1978). Extensions of the model to complex alloy systems have been considered. As an interesting application we may mention the discussion on the stabilities of ternary compounds presented by de Boer et al. (1988). In the case of the Heusler-type alloys XY2Z, for instance, the stability conditions with respect to mechanical mixtures of the same nominal composition (XY2+Z, X+Y2Z, XY+YZ, etc.) have been systematically examined and presented by means of diagrams. The Miedema s parameters, A t>, A ws1/3, moreover, have been used as variables for the construction of structural maps of intermetallic phases (Zunger 1981, Rajasekharan and Girgis 1983). 

The extension of the quantum-mechanic interpretation of the vibrational motion of atoms to a crystal lattice is obtained by extrapolating the properties of the diatomic molecule. In this case there are 3 ( independent harmonic oscillators (9l is here the number of atoms in the primitive unit cell—e.g., fayalite has four... 

Saeva FD (1990) Photoinduced Electron Transfer (PET) Bond Cleavage Reactions. 156 59-92 Sahni V (1996) Quantum-Mechanical Interpretation of Density Functional Theory. 182 1-39 Sakai S,see Inokuma S (1994) 172 87-118 Sandanayake KRAS, see Bissel RA (1993) 168 223-264... 

Our chapter has two broad themes. In the first, we will consider some aspects of quantum states relevant to electrochemical systems. In the second, the theme will be the penetration of the barrier and the relation of the current density (the electrochemical reaction rate) to the electric potential across the interface. This concerns a quantum mechanical interpretation of Talel s experimental work of 1905, which led (1924-1930) to the Butler-Volmer equation. 

Nuclear Quadrupole Coupling Data, Quantum-Mechanical Interpretation of (Scrocco).5 319... 

PHYSICAL CHEMISTRY. Application of the concepts and laws of physics to chemical phenomena in order to describe in quantitative (mathematical) terms a vast amount of empirical (observational) information. A selection of only the most important concepts of physical chemistiy would include the electron wave equation and the quantum mechanical interpretation of atomic and molecular structure, the study of the subatomic fundamental particles of matter. Application of thermodynamics to heats of formation of compounds and the heats of chemical reaction, the theory of rate processes and chemical equilibria, orbital theory and chemical bonding. surface chemistry (including catalysis and finely divided particles) die principles of electrochemistry and ionization. Although physical chemistry is closely related to both inorganic and organic chemistry, it is considered a separate discipline. See also Inorganic Chemistry and Organic Chemistry. 

Sahni, V. Quantum-Mechanical Interpretation of Density Functional Theory. 182,1 -39 (1996). 

Quantum-Mechanical Interpretation of Density Functional Theory... 

In the earlier sections of this chapter we reviewed the many-electron formulation of the symmetry-adapted perturbation theory of two-body interactions. As we saw, all physically important contributions to the potential could be identified and computed separately. We follow the same program for the three-body forces and discuss a triple perturbation theory for interactions in trimers. We show how the pure three-body effects can be separated out and give working equations for the components in terms of molecular integrals and linear and quadratic response functions. These formulas have a clear, partly classical, partly quantum mechanical interpretation. The exchange terms are also classified for the explicit orbital formulas we refer to Ref. (302). 

Dennison, Hardy, and Uhlenbeck presented the first quantum mechanical interpretation of the inversion phenomena in ammonia in the early thirties. Fermi was among the first theoreticians to study this problem his paper on the effect of the centrifugal distortion on the inversion splitting in NH3 was written in 1932 and after 45 years it is still interesting. 

Symmetry is an important but often elusive molecular property when numerical values must be assigned. However, symmetry plays an important role in the quantum mechanical interpretation of atomic and molecular states, NMR spectra and several physico-chemical properties. Symmetry is closely related to those molecular properties which also depend on entropy contributions, such as, for example, melting point, vapour pressure, surface tension, and - dipole moment. Moreover, the nature of overall molecular shape depends on molecular symmetry. 

The quantum mechanical interpretation of the width of the natural spectral line should be based on this relation, in which the physical quantities A and A t =/3 1 have a precise meaning. In our model, the natural line width occurs at wavelength A and can be calculated as... 

Recalling the quantum-mechanical interpretation of the wave function as a probability-amplitude, we see that a product form of the many-body wave function corresponds to treating the probability amplitude of the many-electron system as a product of the probability amplitudes of individual electrons (the orbitals). Mathematically, the probability of a composed event is only equal to the probability of the individual events if the individual events are independent (i.e., uncorrelated). Physically, this means that the electrons described by the product wave function are independent. Such wave functions thus neglect the fact that, as a consequence of the Coulomb interaction, the electrons try to avoid each other. The correlation energy is the additional energy lowering obtained in a real system due to the mutual avoidance of the interacting electrons. 

Compounds. Theoretical estimates of 5p by CNDO/2 calculations required the inclusion of phosphorus adjustable parameter which depends on the type of compound, e.g. phosphine or phosphite. The chemical shifts of a series of cyano-compounds (5 X, Y=hal or CN) agree with those predicted by Letcher and van Wazer s quantum-mechanical interpretation. The sensitivity of 5p to stereochemical changes often leads to quite large differences of chemical shift between various conformers or isomers, e.g. the axial conformer (6) has <5p upheld... 

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