Showing papers on "Quantum published in 1969"

Time-Dependent Semiclassical Scattering Theory. II. Atomic Collisions

Abstract: We derive "classical" equations for the relative motion of two atoms as their insides make a given quantum transition. The classical changes in relative energy and angular momentum associated with this description just balance the corresponding quantum changes in internal energy and angular momentum for the transition involved. The work is based on a generalization of Hamilton's principle, suggested in a natural way by Feynman's formulation of quantum mechanics; the semiclassical scattering theory which emerges is, in essence, a justification and extension of the impact-parameter method. Applications to low-energy atomic collisions are discussed briefly.

Some conformation problems for long macromolecules

Abstract: The statistical mechanics of long flexible chains somewhat benefit from an analogy where a chain configuration is interpreted as one path for a quantum mechanical particle. For instance: (i) the problem of a long chain weakly bound to an adsorbing surface is reminiscent of the ground state of the deuteron, where its wave function extends at distances much longer than the attractive potential; (ii) the coupling between both strands in partially denatured deoxyribonucleic acid is equivalent to a two-body scattering problem (including bound states). The mathematical principles of this correspondence are described here.

Derivation of the Blackbody Radiation Spectrum without Quantum Assumptions

Abstract: The Planck radiation law for the blackbody radiation spectrum is derived without the formalism of quantum theory. The hypotheses assume (a) the existence, at the absolute zero of temperature, of classical homogeneous fluctuating electromagnetic radiation with a Lorentz-invariant spectrum; (b) that classical electrodynamics holds for a dipole oscillator; (c) that a free particle in equilibrium with blackbody radiation has the classical mean kinetic energy $\frac{1}{2}\mathrm{kT}$ per degree of freedom. The Lorentz invariance of the spectrum of zero-temperature radiation is used to derive the zero-point electromagnetic energy-density spectrum, found to be linear in frequency, $\frac{1}{2}\ensuremath{\hbar}\ensuremath{\omega}$ per normal mode. The procedures based on classical theory employed by Einstein and Hopf, which were formerly regarded as giving a rigorous derivation of the Rayleigh-Jeans radiation law, are modified and corrected for electromagnetic zero-point energy to allow a rigorous derivation of the full blackbody spectrum from classical theory without any assumptions of discrete or discontinuous processes.

Theory of filters

Abstract: We consider the following statistical problem: suppose we have a light beam and a collection of semi-transparent windows which can be placed in the way of the beam. Assume that we are colour blind and we do not possess any colour sensitive detector. The question is, whether by only measurements of the decrease in the beam intensity in various sequences of windows we can recognize which among our windows are light beam filters absorbing photons according to certain definite rules? To answer this question a definition of physical systems is formulated independent of “quantum logic” and lattice theory, and a new idea of quantization is proposed. An operational definition of filters is given: in the framework of this definition certain nonorthodox classes of filters are admissible with a geometry incompatible to that assumed in orthodox quantum mechanics. This leads to an extension of the existing quantum mechanical structure generalizing the schemes proposed by Ludwig [10] and the present author [13]. In the resulting theory, the quantum world of orthodox quantum mechanics is not the only possible but is a special member of a vast family of “quantum worlds” mathematically admissible. An approximate classification of these worlds is given, and their possible relation to the quantization of non-linear fields is discussed. It turns out to be obvious that the convex set theory has a similar significance for quantum physics as the Riemannian geometry for space-time physics.

Modern State of the Multiplet Theor of Heterogeneous Catalysis

Abstract: Publisher Summary This chapter reviews the modern state of the multiplet theory of heterogeneous catalysis The multiplet theory deals with numerical values of bond lengths and bond energies, as well as with the geometrical form of reacting molecules and the crystal lattices of catalysts This allows definite results to be obtained for many reactions on an atomic level This is how the multiplet theory differs from a number of other theories on catalysis The theory of the structure of matter is based on both electronic theory and quantum mechanics—the basis for the multiplet theory Bond lengths and energies represent a stable complex of electronic properties essential for catalysis The multiplet theory proceeds from the premise that catalysis is a chemical phenomenon and that covalent bonds require catalytic activation

Radiative Decay of Polyatomic Molecules

Abstract: In this paper we present a quantum‐mechanical treatment of the radiative decay of polyatomic molecules. The decay of a manifold of closely spaced coupled levels is handled by applying the Green's function formalism for the transition probability, where the matrix elements are displayed in an energy representation which involves either the Born–Oppenheimer or the molecular eigenstate basis set. General criteria are obtained for the occurrence of an irreversible intramolecular electronic relaxation process. The features of radiationless transitions in large, medium‐sized, and small molecules are elucidated, deriving general expressions for the radiative decay times and for the fluorescence quantum yields. Some possibilities for studying radiative interference effects in intersystem crossing are explored. A general theoretical demonstration of the occurrence of long radiative lifetimes of small molecules is presented.

Quantum-Mechanical Equation of State of a Hard-Sphere Gas at High Temperature. II

Abstract: As the continuation of a preceding paper, an expansion for the quantum-mechanical free energy F of a hard-sphere gas at high temperature is extended up to the second order in the thermal wavelength X= (27(h /mkT), To reach this order, one must study the three-body problem in a lowest-order approximation, in which adjacent sphere surfaces can be regarded as parallel planes. Coefficients of the X series for F are given in terms of classical correlation functions. Using known density expansions for these correlation functions, one can obtain X expansions for the virial coefficients; the third virial coefficient is

Perturbation theory of fluids and deviations from classical behavior

Abstract: The effects of quantum deviations from classical behavior of simple fluids are examined using the recently developed perturbation theory of fluids. The free energy is expanded in powers of Planck's constant and in powers of the strength of the attractive potential about an unperturbed system of hard spheres whose diameter is chosen to take into account the softness of the repulsive potential. Using the 6:12 potential, the theory is applied to gaseous helium and hydrogen with good results, and to liquid neon with satisfactory results.

Classical Calculations of Linear Reactive Systems: H+Cl2→HCl+Cl

Abstract: Classical trajectory calculations were performed for the collinear H+Cl2 system using reaction coordinates and the potential‐energy surfaces described previously for the quantum calculations. The resulting probabilities of reaction and the vibrational‐energy distributions were compared with previous quantum calculations.

Exact generalized fokker--planck equation for arbitrary dissipative and nondissipative quantum-systems.

Abstract: We start from a density matrix equation in its most general form. It comprises the action of external fields on the system, internal interactions, as well as the action of dissipative mechanisms (heat-baths or reservoirs), which may be Markoffian or non-Markoffian. We then define a distribution function of a type introduced previously byHaken, Risken, Weidlich for atoms. This distribution function,f, which is now formulated quite generally with aid of projection operators,P ik , establishes a connection between theP ik 's and classical variablesv ik . By means off it is possible to exactly calculate all quantum mechanical expectation values by purec-number procedures. If the basic density matrix equation is Markoffian, it is even possible to calculate all time-ordered multitime averages byc-number procedures usingf, as had been demonstrated byHaken, Risken andWeidlich. In the present paper we derive in an explicit way an exactc-number partial differential equation forf. It contains derivatives of arbitrarily high order. In important classes of problems, it can be reduced to an ordinary FokkerPlanck equation, however. Our new equation has many applications, e.g. in the quantum theory of lasers, nonlinear quantum optics, spinresonance, and spin-wave-theory, as will be demonstrated in forthcoming papers. We wish to thank Prof. W.Weidlich and Dipl. Phys. H.Vollmer for several valuable discussions. In addition, H.Vollmer has kindly checked our calculations.

Griffiths' Theorems for the Ferromagnetic Heisenberg Model

Abstract: It is shown that for the quantum mechanical Heisenberg ferromagnet, the correlation is not necessarily a monotone increasing function of interactions.

Quantum and classical size effects in the thermoelectric power of thin bismuth films

Abstract: Anomalous behaviour of the thermoelectric power of thin Bi films has been observed and the results are consistent with those anticipated, based on both quantum and classical size effects in scattering. Mayer's theory relating thermoelectric power to film thickness can be applied to the present results provided that the bulk conduction electron mean free path is used for calculations of the thermoelectric power of thick specimens and that the conduction electron de Broglie wavelength is used for thin specimens.

Macroscopic Quantum Electrodynamics

Abstract: The quantities which relate the propagation of the electromagnetic field variables to experimentally measurable quantities are the expectation values of products of the field operators, 〈a(1)〉, 〈a(1)a(2)〉, etc., where a(1) denotes the vector potential at space–time point 1. These expectation values can be evaluated from a suitably defined generating functional. The set of equations which determines this functional in the presence of matter is particularized to the case in which matter exhibits a linear response to the transverse components of the radiation field. An explicit form is found for the generating functional, and in this linear realm, the close similarity of the propagation of the quantum fields to that determined by the classical phenomenological equations is pointed out. In the case in which matter exhibits a nonlinear response to the radiation field, the equations which determine the generating functional are reduced to an equation of motion for the expectation value of the vector potential. ...

Coupled‐Channels Approach to the Quantum‐Mechanical Treatment of Chemical Exchange Reactions

Abstract: A formalism for the quantum‐mechanical treatment of chemical exchange reactions of the type A+BC→AB+C based on the coupled‐channels technique of solving the Schrodinger equation is developed. Essentially, the method consists of expanding the stationary‐state wavefunction describing the reaction as a linear combination of linearly independent functions satisfying the relevant Schrodinger equation and also initial conditions specified on a “surface” of a particular arrangement channel. These linearly independent functions are generated by integrating the close‐coupled equations throughout the various arrangement channels successively for linearly independent sets of initial conditions. The formalism is explicitly derived for collinear, electronically adiabatic encounters below the three‐particle threshold. It is then applied to a simplified model for symmetric exchange reactions in which the center atom is very massive. The calculated transition and reaction probabilities are in agreement with recently reported results for the same model.

Opening remarks: quantum‐mechanical calculations of biological structures and mechanisms

Abstract: It is an honor and a pleasure for me to open the International Conference on the Electronic Aspects of Biochemistry. Although one of the youngest, it is also one of the most dynamic branches of modem biochemistry. The fact that The New York Academy of Sciences has selected this subject for one of the meetings held in celebration of the sesquicentennial year of its founding underlines both the maturity and the actuality of this field of research. The first general symposium on this subject, sponsored by NATO, was held in Ravello, Italy, about four years ago in September, 1963. I do not doubt that a comparison of the results of our present meeting with the proceedings of the Ravello symposium will certainly show the important progress achieved during these last few years. The electronic aspects of biochemistry are being explored both by a series of modem experimental techniques such as the nuclear magnetic resonance or the electron-spin resonance, and by theoretical methods based on quantum mechanics, so that the new and-to some people-still somewhat puzzling designation of “quantum biochemistry” recently entered the scientific vocabulary. Scientists more qualified than myself will describe the utilization of a variety of experimental techniques for the elucidation of the submolecular, electronic aspects of biochemistry. In these introductory remarks I should like to make only a few general comments on the quantum-mechanical aspects of these investigations. The purpose of quantum biochemistry is to apply the general ideas and methods of wave-mechanics to the study of the electronic structure of biological molecules in relation to their behavior as substrates of life, i.e., to their involvement in the biochemical and biophysical processes characteristic of the living matter. A similar penetration of quantum-mechanical ideas and methods has already been accomplished some time ago in organic and physical organic chemistry, and has resulted in an extraordinary enrichment of these disciplines. The enrichment concerned in particular the deeper understanding in the appropriate terms of the nature of the electronic factors responsible for the structural and dynamic properties of organic compounds. It resulted in new concepts, daring suggestions and predictions all of which stimulated the remarkable blooming of that discipline. It may therefore seem strange, at first sight at least, that the similar penetration of these powerful and obviously fruitful ideas and techniques into biochemistry has been delayed for so long and, in fact, only started in a systematic and quantitative way about ten years ago. The explanation of this puzzle probably lies in the mutual ignorance of biochemistry by quantum chemists and of quantum chemistry by biochemists. In my opinion, the fault in this respect lies more on the side of the quantum chemists than of the biochemists. Of course, the relative complexity of the biological molecules and processes,

Quantum Liquids. II. Microscopic Theory of Liquid He 3 -He 4 Mixtures

Abstract: We calculate the equilibrium and transport properties of the mixtures using the overcomplete basis functions ${\ensuremath{\phi}}^{k}{\ensuremath{\psi}}_{q}$ discussed in I. The theory includes the enlarged correlation hole of a single ${\mathrm{He}}^{3}$ and the backflow of ${\mathrm{He}}^{4}$ atoms around it. The two quasiparticle scattering amplitude is the sum of two terms $V=\ensuremath{-}{\ensuremath{\alpha}}^{2}\frac{{m}_{4}{s}^{2}}{n}\ensuremath{-}\frac{{\ensuremath{\hbar}}^{2}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})({\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}^{\ensuremath{'}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})}{{m}_{4}n{q}^{2}}{\left(\frac{(1+\ensuremath{\alpha}){m}_{4}+\ensuremath{\delta}m}{{m}_{3}+\ensuremath{\delta}m}\right)}^{2}$ the first from the interaction of the excess correlation holes and the second from the interaction of the backflows. Both terms were derived previously from macroscopic considerations by Bardeen, Baym, and Pines.

Quantum Interference Paradox

Abstract: THE development of atomic time standards and high-speed recording techniques has allowed the extension of radio interferometry to baselines extending thousands of miles. The amplitude, rather than the power, of the received radiation is recorded separately at two or more stations with accurate time control, and the interference pattern is later recovered by cross-correlating the signals by digital1,2 or analogue3 methods. The measurements are usually described in classical terms, for the observations are well outside the domain of quantum phenomena. A discussion of the technique in quantum terms, however, raises an interesting form of the quantum interference paradox that Einstein, Bohr and others debated so vigorously4 40 years ago, in the discussion of the two-slit interference pattern shown in Fig. la. Any attempt to determine which slit a photon or an electron passes through must result in the destruction of the interference pattern.