Quantum Mechanical Approximation Research Articles

Electromagnetic field generation by ATP-induced reverse electron transfer

This paper describes a mechanism to explain low-level light emission in biology. A biological analog of the electrical circuitry, modeled on the parallel plate capacitor, traversed by a helical structure, required to generate electromagnetic radiation in the optical spectral range, is described. The charge carrier required for the emissions is determined to be an accelerating electron driven by an ATP-induced reverse electron transfer. The radial velocity component, the emission trajectory, of the moving charges traversing helical protein structures in a cyclotron-type mechanism is proposed to be imposed by the ferromagnetic field components of the iron in the iron–sulfur proteins. The redox systems NADH, riboflavin, and chlorophyll were examined with their long-wavelength absorption maxima determining the energetic parameters for the calculations. Potentials calculated from the axial velocity components for the riboflavin and NADH systems were found to equal the standard redox potentials of these systems as measured electrochemically and enzymatically. The mechanics for the three systems determined the magnetic moments, the angular momenta, and the orbital magnetic fluxes to be adiabatic invariant parameters. The De Broglie dual wave–particle equation, the fundamental equation of wave mechanics, and the key idea of quantum mechanics, establishes the wavelengths for accelerating electrons which, divided into a given radial velocity, gives its respective emission frequency. Electrons propelled through helical structures, traversed by biologically available electric and magnetic fields, make accessible to the internal environment the optical spectral frequency range that the solar spectrum provides to the external environment.

Investigating the Adiabatic Approximation in Quantum Mechanics through the Analysis of Two Coupled Harmonic Oscillators

The nature of the adiabatic approximation is investigated. This approximation is at the center of the Born-Oppenheimer approximation, commonly employed in the construction of molecular potentials. First, general behaviors of the approximation and some implications of these results are discussed. We show that the ground-state energy, calculated using the adiabatic approximation, will be lower than the calculated energy when no approximations are made. Next, a numerical and analytical application of the adiabatic approximation to systems comprising two coupled harmonic oscillators is described. These systems are used to demonstrate the results derived in the first part of the paper and to investigate how the accuracy of the approximation depends on the frequencies of the oscillators and the coupling strength.

Zero-point angular momentum of supersymmetric Penning trap

The quantum behavior of supersymmetric Penning trap, specially the superpartner of its angular momentum, is investigated in the formulation of multi-dimensional semiunitary transformation of supersymmetric quantum mechanics. In the limit case of vanishing kinetic energy it is found that its lowest angular momentum is 3ℏ/2, which provides a possibility of directly checking the idea of supersymmetric quantum mechanics and thus suggests a possible experimental verification about this prediction.

State vector reduction as a shadow of a noncommutative dynamics

A model, based on a noncommutative geometry, unifying general relativity and quantum mechanics, is developed. It is shown that the dynamics in this model can be described in terms of one-parameter groups of random operators, and that the noncommutative counterparts of the concept of state and that of probability measure coincide. We also demonstrate that the equation describing noncommutative dynamics in the quantum mechanical approximation gives the standard unitary evolution of observables, and in the “space–time limit” it leads to the state vector reduction. The cases of the spin and position operators are discussed.

Quantum associative memory

This paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm. Quantum computation (QC) uses microscopic quantum level effects to perform computational tasks and has produced results that in some cases are exponentially faster than their classical counterparts. The unique characteristics of quantum theory may also be used to create a quantum associative memory (QuAM) with a capacity exponential in the number of neurons. This paper combines two quantum computational algorithms to produce such a quantum associative memory. The result is an exponential increase in the capacity of the memory when compared to traditional associative memories such as the Hopfield network. The paper covers necessary high-level quantum mechanical and quantum computational ideas and introduces a QuAM. Theoretical analysis proves the utility of the memory, and it is noted that a small version should be physically realizable in the near future.

Continued fraction representation of the Coulomb Green’s operator and unified description of bound, resonant and scattering states

If a quantum-mechanical Hamiltonian has an infinite symmetric tridiagonal (Jacobi) matrix form in some discrete Hilbert-space basis representation, then its Green's operator can be constructed in terms of a continued fraction. As an illustrative example we discuss the Coulomb Green's operator in a Coulomb-Sturmian basis representation. Based on this representation, a quantum-mechanical approximation method for solving Lippmann-Schwinger integral equations can be established, which is equally applicable for bound-, resonant- and scattering-state problems with free and Coulombic asymptotics as well. The performance of this technique is illustrated with a detailed investigation of a nuclear potential describing the interaction of two $\ensuremath{\alpha}$ particles.

A non-perturbative chiral approach for meson-meson interactions

A non-perturbative method which combines constraints from chiral symmetry breaking and coupled channel unitarity is used to describe meson-meson interactions up to \sqrt{s}\lesssim 1.2 GeV, extending in this way the range of applicability of the information contained in Chiral Perturbation Theory (\chi PT), since this perturbative series is typically restricted to \sqrt{s}\lesssim 500 MeV. The approach uses the O(p^2) and O(p^4) \chiPT Lagrangians. The seven free parameters resulting from the O(p^4) Lagrangian are fitted to the experimental data. The approach makes use of the expansion of T^{-1} instead of the amplitude itself as done in \chiPT. The former expansion is suggested by analogy with the effective range approximation in Quantum Mechanics and it appears to be very useful. The results, in fact, are in good agreement with a vast amount of experimental analyses.

Non-stationary scattering of wave-packets

Potential scattering of free-electron wave packets is considered in the framework of non-stationary quantum-mechanical theory. The general expression for the average angle of scattering is obtained. The traditional quantum-mechanical plane-wave approximation and classical results are shown to be incorporated in the results derived.

Chaos in time-dependent variational approximations to quantum dynamics

@Dynamical chaos has recently been shown to exist in the Gaussian approximation in quan-tum mechanics and in the self-consistent mean field approach to studying the dynamics ofquantum fields. In this study, we first show that any variationalapproximationto the dynam-ics of a quantum system based on the Dirac action principle leads to a classical Hamiltoniandynamics for the variational parameters. Since this Hamiltonian is generically nonlinearand nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exactquantum evolution. We then restrict attention to a system of two biquadratically coupledquantum oscillators and study two variational schemes, the leading order large N (fourcanonical variables) and Hartree (six canonical variables) approximations. The chaos seenin the approximate dynamics is an artifact of the approximations: this is demonstrated bythe fact that its onset occurs on the same characteristic time scale as the breakdown of theapproximations when compared to numerical solutions of the time-dependent Schr¨odingerequation.PACS numbers: 05.45. +b, 03.65. Sq, 2.30 Wd, 03.65 -w

Probability distributions and coherent states of , and algebras

A new approach to probability theory based on quantum mechanical and Lie algebraic ideas is proposed and developed. The underlying fact is the observation that the coherent states of the Heisenberg-Weyl, su(2), , and algebras in certain symmetric (bosonic) representations give the `probability amplitudes' (or the `square roots') of the well known Poisson, binomial, multinomial, negative binomial and negative multinomial distributions in probability theory. New probability distributions are derived based on coherent states of the classical algebras , and in symmetric representations. These new probability distributions are simple generalization of the multinomial distributions with some added new features reflecting the quantum and Lie algebraic construction. As byproducts, simple proofs and interpretation of addition theorems of Hermite polynomials are obtained from the `coordinate' representation of the (negative) multinomial states. In other words, these addition theorems are higher rank counterparts of the well known generating function of Hermite polynomials, which is essentially the `coordinate' representation of the ordinary (Heisenberg-Weyl) coherent state.

An adiabatic approximation for grain alignment theory

The alignment of interstellar dust grains is described by the joint distribution function for certain ``internal'' and ``external'' variables, where the former describe the orientation of a grain's axes with respect to its angular momentum, J, and the latter describe the orientation of J relative to the interstellar magnetic field. I show how the large disparity between the dynamical timescales of the internal and external variables--- which is typically 2--3 orders of magnitude--- can be exploited to greatly simplify calculations of the required distribution. The method is based on an ``adiabatic approximation'' which closely resembles the Born-Oppenheimer approximation in quantum mechanics. The adiabatic approximation prescribes an analytic distribution function for the ``fast'' dynamical variables and a simplified Fokker-Planck equation for the ``slow'' variables which can be solved straightforwardly using various techniques. These solutions are accurate to order epsilon, where epsilon is the ratio of the fast and slow dynamical timescales. As a simple illustration of the method, I derive an analytic solution for the joint distribution established when Barnett relaxation acts in concert with gas damping. The statistics of the analytic solution agree with the results of laborious numerical calculations which do not exploit the adiabatic approximation.

A quasiclassical and approximate quantum mechanical study of the intramolecular isotope effect in proton transfer elementary reactions: the Ne + HD+ → NeH+(NeD+) + D(H) system at low and moderate collision energies (0.02–0.77 eV)

The quasiclassical trajectory method (QCT) and the quantum mechanical (QM) reactive infinite order sudden approximation (R-IOSA) method have been applied to study the dependence of the isotope effects in the Ne + H2+ reaction with the relative translational energy (Etras) and vibrational energy of the molecular ion, dedicating particular attention to the intramolecular isotope effect. To do this, we have used two different analytical functions to represent the ground NeH2+(2A′) potential energy surfaces (PES). The intramolecular isotope branching ratio is essentially constant and equal to unity in the Etras range considered (0.02–0.77 eV) and the QCT results are in good agreement with a mass spectrometric experiment. The R-IOSA results also agree with the experimental data but at higher collision energies. However, the theoretical approach, using a single PES, to the reaction generated after the chemiionization of the HD molecule by a metastable Ne atom has been unable to reproduce the experimental intramolecular isotope effect value, σ(NeH+)/σ(NeD+), of 0.67. A detailed analysis of the QCT reaction dynamics at low Etras (0.02–0.08 eV) for both reaction channels, considering scalar and vector properties and carried out using the most accurate PES available, suggests that at the very low Etras values mainly involved when the reaction arises from chemiionization of HD, the Ne + HD+ dynamics is essentially unimolecular and the density of states play a dominant role in the intramolecular branching ration, favoring the formation of the NeD+ product over the NeH+ one.

From the quantum random walk to classical mesoscopic diffusion in crystalline solids.

We use a discrete approximation of quantum mechanics called the quantum random walk to study diffusion in one-dimensional crystalline nanostructures. There, intense fluctuations in the density are a consequence of quantum interference. As the size of the crystal increase, relative quantum fluctuations decrease and, if a coarse-grained averaging is taken, interference may be neglected. When this happens, we describe a far-from-equilibrium, classical, dynamic mesoscopic diffusion regime. In this regime, diffusion equations are given by a persistent-random-walk process. Density becomes a second-order Markov process, and in the continuum limit, the current satisfies the non-Fickian Maxwell-Cattaneo relationship. The generalized diffusion equation in the telegraphist's equation.

Quantum mechanical models in catalysis

We applied general quantum mechanical ideas in order to establish the form of the many-electron wave functions suitable for analysis of catalytic processes. This led us to the conclusion that the relevant wave functions for the electrons of the catalytic complexes must be taken as superpositions of the antisymmetrized products of the wave functions of electrons in excited and ionized states of the catalyst and reactants. With use of the trial wave function for the electrons of the catalytic complex in such a form, it becomes possible to construct model potential energy surfaces of catalytic reactions as a superposition of the potential energy surfaces of the reactants in different electronic states. We formulate the criteria which when satisfied make it possible to implement a catalytic version of a desired chemical transformation. We also propose an approach to the explanation of the frequently observed correlations between the catalytic activity and other physical properties of a catalyst. © 1996 John Wiley & Sons, Inc.

Circular dichroism from non-chiral and non-magnetic materials observed with display-type spherical mirror analyzer

Strong circular dichroism in 2-dimensional photoelectron diffraction patterns was observed for the photoelectron from the Si 2p core on the Si(001) surface using a display-type spherical mirror analyzer, although this Si(001) surface has no chirality and magnetism. The forward focusing peaks in the pattern rotate in the same direction as the incident light, i.e., clockwise or counterclockwise when the helicity of the incident circularly polarized light is reversed. These rotations of the pattern are explained by the phenomenon that the wave-front of the photoelectron wavefunction rotates as it propagates outward. This is the first direct observation of the rotation of the wavefront of the electronic wavefunction and clarifies the correspondence between the classical and the quantum mechanical ideas of angular momentum. This phenomenon offers a new possibility to measure the three dimensional surface structure.

Polyexponential kinetics of chemical reactions in condensed media within the quasiclassical approximation

Polyexponential kinetical behavior typical for condensed phase reactions in highly viscous media is studied on a simple example of one-dimensional diffusion equation with a sink modeling a chemical conversion of reactants. The corresponding polyexponential regime is demonstrated to have a thorough analogy with the quasiclassical approximation of one-dimensional quantum mechanics and a relevant approximation for the Green’s function is developed. The asymptotic short- and long-time kinetics are examined at the analytical level. Contrary to the frozen medium approximation according to which the slow diffusion motion of the medium is entirely ignored, the present quasiclassical model is fit for a qualitative description of the total time interval covering the reaction events from the initial moment up to the ultimate steady-state monoexponential evolution. The range of validity of the quasiclassical approach is discussed. Numerical tests expose some peculiarities of the present treatment for equilibrium and nonequilibrium initial distributions. The work presents a qualitative development of the theory of nonexponential kinetics pioneered by papers of Agmon and Hopfield, Sumi and Marcus, and Nadler and Marcus.

A semiclassical approach to the calculation of electron impact ionization cross-sections of atoms: From hydrogen to uranium

Absolute ionization cross-sections for single ionization by electron impact (from threshold up to 200 eV) of free gaseous atoms have been calculated by utilizing a recently proposed semiclassical approach (DM formulation). The formula used here is derived within the framework of classical and quantum mechanical approximations, and the necessary input parameters are determined and discussed. Where possible the calculated ionization cross-section functions are compared with experimental data sets and with the most widely used previous formulae such as the Gryzinski and Lotz formulae. It is concluded that the present approach leads on average to a better agreement with experimental results than previous classical, semiclassical and empirical treatments.

A semiclassical approach to the calculation of electron impact ionization cross-sections of atoms: from hydrogen to uranium

Absolute ionization cross-sections for single ionization by electron impact (from threshold up to 200 eV) of free gaseous atoms have been calculated by utilizing a recently proposed semiclassical approach (DM formulation). The formula used here is derived within the framework of classical and quantum mechanical approximations, and the necessary input parameters are determined and discussed. Where possible the calculated ionization cross-section functions are compared with experimental data sets and with the most widely used previous formulae such as the Gryzinski and Lotz formulae. It is concluded that the present approach leads on average to a better agreement with experimental results than previous classical, semiclassical and empirical treatments.

The semiclassical approximation in quantum mechanics. A new approach

It is shown that the semiclassical approximation in quantum mechanics is equivalent to replacement of the Schrodinger equation by a finite closed system of first-order ordinary differential equations with initial conditions that satisfy special restrictions.

Transition from quantum to quasi-classical behaviour of the binary encounter peak in collisions of 0.6 to 3.6 MeV amu-1 I23+ and Xe21+ with He and Ar

Double differential cross sections are reported for the production of binary encounter electrons in collisions of 0.6 MeV amu-1 I23+ and 1.4, 2.4, and 3.6 MeV amu-1 Xe21+ projectiles incident on He and Ar targets. Electron energy spectra were measured between 0 degrees and 45 degrees in the case of the two lower projectile energies, and between 17.5 degrees and 60 degrees for the two higher projectile energies. The data are compared with quantum mechanical impulse approximation and classical trajectory Monte Carlo calculations. While the quantum model calculation predicts a rapid disappearance of diffraction effects in the binary encounter peak with increasing projectile energy, these remain visible in the experimental results up to the highest energy measured. The necessity of including multiple target ionization involving inner shell electrons in the theoretical description of the collision process is demonstrated by the classical trajectory Monte Carlo calculation, which accounts well for the shape of the 2.4 and 3.6 MeV amu-1 cross sections, except at angles where diffraction effects are manifest. Systematic shifts of the binary encounter peak position towards lower energies with increasing emission angle were observed for all projectile energies.