On the Feynman integral for classical waves.
Feynman integral for classical waves evaluated, using Hamiltonian approach to summation
INTEGRAL FUNCTION↗
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Feynman functional integrals for systems of indistinguishable particles
Feynman path integration for multiply connected space systems of indistinguishable particles, considering bosons and fermions propagators
Dewitt, C. M.↗
Integrated and integral Hellmann-Feynman formulas.
Integrated and integral Hellmann-Feyman formulas for isoelectronic molecular process energy difference
FEYNMAN DIAGRAM↗
Dissociation of diatomic molecules from the viewpoint of the integral Hellmann-Feynman formula- H2, LiH, and Li2
Integral Hellmann-Feynman formula for dissociation energies in H, Li and LiH molecules, discussing transition densities and dissociation energy
Marron, M. T.↗
Fourier transform of the multicenter product of 1s hydrogenic orbitals and Coulomb or Yukawa potentials and the analytically reduced form for subsequent integrals that include plane waves
The Fourier transform of the multicenter product of N 1s hydrogenic orbitals and M Coulomb or Yukawa potentials is given as an (M+N-1)-dimensional Feynman integral with external momenta and shifted coordinates. This is accomplished through the introduction of an integral transformation, in addition to the standard Feynman transformation for the denominators of the momentum representation of the terms in the product, which moves the resulting denominator into an exponential. This allows the angular dependence of the denominator to be combined with the angular dependence in the plane waves.
Straton, Jack C.↗
Integral Hellmann-Feynman analysis of the binding energy of H2 and LiH using atomic reference states
Integral Hellman-Feynman formula applied to binding energy of molecular H and LiH, using SCF wavefunctions for atomic states
Marron, M. T.↗
Internuclear separation derivatives of the energy of a diatomic molecule.
Higher order derivatives of energy with respect to internuclear separation for diatomic molecules derived from ordinary and integral Hellmann- Feynman theorems
Kim, H.↗
Self-consistent Green's-function approach to the electron-gas problem
Electron gas problem in metal physics by self consistent Green function formalism, presenting momentum-space Feynman rules and integral equations derivation
Zmuidzinas, J. S.↗
Solar proton events during solar cycles 19, 20, and 21
Earlier studies based on a single solar cycle had resulted in a sharp division of events into 'ordinary' and 'anomalously large' events. Two such entirely separate distributions imply two entirely separate acceleration mechanisms, one common and the other very rare. The sharp division is neither required nor justified by this larger sample. Instead the event intensity forms a smooth distribution for intensities up to the largest observed implying that any second acceleration mechanism cannot be rare. Also, a clear bimodal variation of annual integrated flux with solar cycle phase but no statistically significant tendency for the large events to avoid sunspot maximum is found. There is almost no relation between the maximum sunspot number in a solar cycle and the solar cycle integrated flux. It is also found that for annual sunspot numbers greater than 35 there is no relation whatsoever between the annual sunspot numbers and annual integrated flux.
Feynman, J.↗
Description of quantum noise by a Langevin equation
General features of the quantum noise problem expressed as the equations of motion for a particle coupled to a set of oscillators are investigated analytically. Account is taken of the properties of the companion oscillators by formulating quantum statistical correlation Langevin equations (QSLE). The frequency of the oscillators is then retained as a natural cut-off for the quantum noise. The QSLE is further extended to encompass the particle trajectory and is bounded by initial and final states of the oscillator. The states are expressed as the probability of existence at the moment of particle collision that takes the oscillator into a final state. Two noise sources then exist: a statistical uncertainty of the initial state and the quantum dynamical uncertainty associated with a transition from the initial to final state. Feynman's path-integral formulation is used to characterize the functional of the particle trajectory, which slows the particle. It is shown that the energy loss may be attributed to friction, which satisfies energy conservation laws.
Metiu, H.↗
Analytically reduced form of multicenter integrals from Gaussian transforms
The four-dimensional Fourier-Feynman transformations previously used in analytically reducing the general class of integrals containing multicenter products of 1s hydrogenic orbitals, Coulomb or Yukawa potentials, and plane waves, are replaced by the one-dimensional Gaussian transformation. This reduces the previously required double-diagonalization of the quadratic form of the multicenter integrals to only one diagonalization, yielding a simpler reduced form of the integral. The present work also extends the result to include all s states and pairs of states with l not equal to zero summed over the m quantum number.
Straton, Jack C.↗
Gauge invariant quantum cosmology
The study of boundary conditions, the Hamiltonian constraint, reparameterization-invariance, and quantum dynamics, is presently approached by means of the path-integral quantization of minisuperspace models. The separation of the wave functions for expansion and contraction by the Feynman boundary conditions is such that there can be no interference between them. This is implemented by the choice of a contour in the complex plane, in order to define the phase of the square-root Arnowitt, Deser, and Misner (1960) Hamiltonian for expansion, collapse, and the classically forbidden region.
Berger, Beverly K.↗
On Whether Angular Momentum in Electric and Magnetic Fields Radiates to Infinity
The Feynman Disk experiment and a related thought experiment with a static magnetic field and capacitor are studied. The mechanical torque integrated over time (angular impulse) is related to the angular momentum in the electric/magnetic field. This is not called an electromagnetic field since quasi-static as well as electromagnetic effects are included. The angular momentum in the electric/magnetic field is examined to determine its static and radiative components. This comparison was then examined to see if it clarified the Abraham-Minkowski paradox.
Canning, Francis X.↗
Functional methods for waves in random media
Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media, and a derivation of approximate moment equations from the functional integral representation.
Chow, P. L.↗
Functional methods for waves in random media
Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media; and a derivation of approximate moment equations from the functional integral representation.
Chow, P. L.↗
A Synthesis of Fluid Dynamics and Quantum Chemistry for the Design of Nanoelectronics
In 1959, during a famous lecture entitled "There's Plenty of Room at the Bottom", Richard Feynman focused on the startling technical possibilities that would exist at the limit of miniaturization, that being atomically precise devices with dimensions in the nanometer range. A nanometer is both a convenient unit of length for medium to large sized molecules, and the root of the name of the new interdisciplinary field of "nanotechnology". Essentially, "nanoelectronics" denotes the goal of shrinking electronic devices, such as diodes and transistors, as well as integrated circuits of such devices that can perform logical operations, down to dimensions in the range of 100 nanometers. The thirty-year hiatus in the development of nanotechnology can figuratively be seen as a period of waiting for the bottom-up and atomically precise construction skills of synthetic chemistry to meet the top-down reductionist aspirations of device physics. The sub-nanometer domain of nineteenth-century classical chemistry has steadily grown, and state-of-the-art supramolecular chemistry can achieve atomic precision in non-repeating molecular assemblies of the size desired for nanotechnology. For nanoelectronics in particular, a basic understanding of the electron transport properties of molecules must also be developed. Quantum chemistry provides powerful computational methods that can accurately predict the properties of small to medium sized molecules on a desktop workstation, and those of large molecules if one has access to a supercomputer. Of the many properties of a molecule that quantum chemistry routinely predicts, the ability to carry a current is one that had not even been considered until recently. "Currently", there is a controversy over just how to define this key property. Reminiscent of the situation in high-Tc superconductivity, much of the difficulty arises from the different models that are used to simplify the complex electronic structure of real materials. A model-independent approach has been proposed, that sacrifices the plentiful molecular orbitals and Bloch functions of conventional approaches, for a single three-dimensional observable quantity, the electron momentum density Pi(sub rho). This quantity is simply the probability of any electron having momentum rho, multiplied by the total number of electrons in the system (the position of the electron is uncertain). We have explored the utility of this new approach in providing a fundamental understanding of the electron transport properties of molecules that have provi been nominated as candidates for components in the design of nanoelectronics; phenylene-ethynylene oligomers. Some of the molecular systems that have been studied are sketched below.
MacDougall, Preston J.↗
Solar energetic particle events: Statistical modelling and prediction
Solar energetic particle events (SEPEs) can have a significant effect on the design and operation of earth orbiting and interplanetary spacecraft. In relation to this, the calculation of proton fluences and fluxes are considered, describing the current state of the art in statistical modeling. A statistical model that can be used for the estimation of integrated proton fluences for different mission durations of greater than one year is reviewed. The gaps in the modeling capabilities of the SEPE environment, such as a proton flux model, alpha particle and heavy ion models and solar cycle variations are described together with the prospects for the prediction of events using neural networks.
Gabriel, S. B.↗