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Electronic wave functions for diatomic lithium hydride molecules, using quantum mechanical calculations
Quantum mechanical treatment of atomic center of mass motion in theory of collision effects on line shapes
The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.
An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.
Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this be consistent with the complexity of our own experiences? In this paper we propose that the experiences of any observer Ob in a closed universe can be approximately described by a quantum mechanical theory with a Hilbert space whose dimension is roughly e S Ob , where S Ob is the number of degrees of freedom of Ob. Moreover we argue that the errors in this description are exponentially small in S Ob . We give evidence for this proposal by incorporating it into the gravitational path integral and the coding interpretation of holography in simple models and seeing that it works, and we explain how similar effects arise in black hole physics in appropriate circumstances.
FORTRAN 4 subroutines for coupling coefficients and matrix elements in quantum mechanical theory of angular momentum
The paper presents a quantum mechanical formalism for treating ionizing collisions occurring in the presence of an intense laser field. Both the intense laser radiation and the internal electronic continuum states associated with the emitted electrons are rigorously taken into account by combining discretization techniques with expansions in terms of electronic-field representations for the quasi-molecule-plus-photon system. The procedure leads to a coupled-channel description of the heavy-particle dynamics which involves effective electronic-field potential surfaces and continua. It is suggested that laser-influenced ionizing collisions can be studied to verify the effects of intense laser radiation on inelastic collisional processes. Calculation procedures for electronic transition dipole matrix elements between discrete and continuum electronic states are outlined.
The variances of the quantum-mechanical noise in a two-input-port Michelson interferometer within the framework of the Loudon-Ni model were solved exactly in two general cases: (1) one coherent state input and one squeezed state input, and (2) two photon number states inputs. Low intensity limit, exponential decaying signal and the noise due to mixing were discussed briefly.
This paper, following a brief introduction, is divided into five parts. Part I outlines the theory of the molecular orbital method for the ground, ionized and excited states of molecules. Part II gives a brief summary of the interaction integrals and their tabulation. Part III outlines an automatic program designed for the computation of various states of molecules. Part IV gives examples of the study of ground, ionized and excited states of CO, BH and N2 where the program of automatic computation and molecular integrals have been utilized. Part V enlists some special problems of Molecular Quantum Mechanics are being tackled at New York University.
Quantum mechanical study of molecules - prediction of ground, ionized, and excited states of unknown nitrogen fluoride molecule
The point form is used as a framework for formulating a relativistic quantum mechanics, with the mass operator carrying the interactions of underlying constituents. A symplectic Lie algebra of mass operators is introduced from which a relativistic harmonic oscillator mass operator is formed. Mass splittings within the degenerate harmonic oscillator levels arise from relativistically invariant spin-spin, spin-orbit, and tensor mass operators. Internal flavor (and color) symmetries are introduced which make it possible to formulate a relativistic SU(6) model of baryons (and mesons). Careful attention is paid to the permutation symmetry properties of the hadronic wave functions, which are written as polynomials in Bargmann spaces.
New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.
The accuracy of current molecular-structure calculations is illustrated with examples of quantum mechanical solutions for chemical problems. Two approaches are considered: (1) the coupled-cluster singles and doubles (CCSD) with a perturbational estimate of the contribution of connected triple excitations, or CCDS(T); and (2) the multireference configuration-interaction (MRCI) approach to the correlation problem. The MRCI approach gains greater applicability by means of size-extensive modifications such as the averaged-coupled pair functional approach. The examples of solutions to chemical problems include those for C-H bond energies, the vibrational frequencies of O3, identifying the ground state of Al2 and Si2, and the Lewis-Rayleigh afterglow and the Hermann IR system of N2. Accurate molecular-wave functions can be derived from a combination of basis-set saturation studies and full configuration-interaction calculations.
Quantum mechanical study of transition probabilities, Einstein A coefficients, and oscillator strengths of band systems of diatomic molecules
The photodissociation dynamics of HBr adsorbed on a LiF(001) surface is studied using time-independent quantum mechanics. The photodissociation lineshape and the Br(P(sub 1/2)-2)/Br(P(sub 3/2)-2) yield ratio are computed and compared with the corresponding quantities for gas phase photodissociation. The angular distribution of the hydrogen photofragments following excitation of adsorbed HBr is computed and found to agree qualitatively with experimental data. The effect of polarization of the photon is illustrated and discussed. The field polarization is found to affect significantly the magnitude of the photodissociation signal but not the angular dependence of the photofragment distribution, in agreement with experiment and in accord with expectations for a strongly aligned adsorbed phase.
The photodissociation dynamics of HBr adsorbed on an LiF(001) surface is studied using time-independent quantum mechanics. The photodissociation line shape and the Br(2P(1/2))/Br(2P(3/2)) yield ratio are computed and compared with the corresponding quantities for gas phase photodissociation. The angular distribution of the hydrogen photofragments following excitation of adsorbed HBr is computed and found to agree qualitatively with experimental data. The effect of polarization of the photon is illustrated and discussed. We find the field polarization to affect significantly the magnitude of the photodissociation signal but not the angular dependence of the photofragment distribution, in agreement with experiment and in accord with expectations for a strongly aligned adsorbed phase.
A new formalism of the generalized Newton variational principle for the calculation of quantum mechanical state-to-state reaction probabilities is presented. The reformulation involves solving directly for the transition matrix rather than the reactance mtrix so that calculations may be carried out for individual columns of the transition matrix without obtaining solutions for all possible initial channels. The convergence of calculations with real and complex boundary conditions are compared for H + H2 - H2 + H, O + H2 - OH + H, and O + HD - OH + D and OD + H.
Collision effects on atomic spectral line profiles, using quantum mechanical description of atomic center-of-mass motion with particular application to lasers