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For a general Hamiltonian appropriate to a single canonical degree of freedom, a universal propagator with the property that it correctly evolves the coherent-state Hilbert space representatives for an arbitrary fiducial vector is characterized and defined. The universal propagator is explicitly constructed for the harmonic oscillator, with a result that differs from the conventional propagators for this system.
Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.
Proper-time relativistic single-particle classical Hamiltonian mechanics is formulated using a transformation from observer time to system proper time which is a canonical contact transformation on extended phase space. It is shown that interaction induces a change in the symmetry structure of the system which can be analyzed in terms of a Lie-isotopic deformation of the algebra of observables.
Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.
The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein-Gordon equation with a potential of the form: (ar(sub 2) + b(L x S)), where a and b are constants. To obtain the Dirac oscillator, a 'minimal substitution' is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, an unusual feature of the covariant derivative in this case is that the potential is a non-trivial element of the Clifford algebra. A theory which naturally gives rise to gage potentials which are non-trivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the automorphism gage field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented.
The information required by a programmer using the Minimum Hamiltonian AScent Trajectory Evaluation (MASTRE) Program is provided. This document enables the programmer to either modify the program or convert the program to computers other than the VAX computer. Documentation for each subroutine or function based on providing the definitions of the variables and a source listing are included. Questions concerning the equations, techniques, or input requirements should be answered by either the Engineering or User's manuals. Three appendices are also included which provide a listing of the Root-Sum-Square (RSS) program, a listing of subroutine names and definitions used in the MASTRE User Friendly Interface Program, and listing of the subroutine names and definitions used in the Mass Properties Program. The RSS Program is used to aid in the performance of dispersion analyses. The RSS program reads a file generated by the MASTRE Program, calculates dispersion parameters, and generates output tables and output plot files. UFI Program provides a screen user interface to aid the user in providing input to the model. The Mass Properties Program defines the mass properties data for the MASTRE program through the use of user interface software.
The pure rotational spectrum of MgH radical (X 2 Sigma (+)) in its ground state v = 0 and v = 1 vibrational modes has been observed in the laboratory using millimeter/submillimeter direct absorption spectroscopy. The rotational spectra of two isotopically substituted species, MgD and (Mg-26)H, have been detected as well. All six hyperfine components of the N = 0 -1 transition of MgH in its v = 0 and v = 1 states have been directly measured to an accuracy of +/-50 kHz, and the five components have been observed for (Mg-26)H. The N = 0 +/-1 and N = 1 -2 transitions of MgD have also been detected. Rotational, fine structure, and hyperfine constants were determined for all species from a nonlinear least-squared fit to the data using a 2 Sigma Hamiltonian.
The nonhomogeneous Clohessy-Wiltshire (C-W) equations are formulated and solved as an initial value problem in the form structure of linear systems theory. The state transition matrix (STM) and its inverse are obtained explicitly in both Newtonian and Hamiltonian form. It is shown that the STM for the C-2 equations possesses a special property making its inverse easily obtainable. Since solutions to the C-W equations are needed in two-point boundary value form to construct a good mission design tool for orbit transfer, the Lambert problem is solved in the context of the C-W equations.
We calculate properties of neutron star matter at subnuclear densities using an improved nuclear Hamiltonian. Nuclei disappear and the matter becomes uniform at a density of about 0.6n(s), where n(s) of about 0.16/cu fm is the saturation density of nuclear matter. As a consequence, the mass of matter in the crusts of neutron stars is only about half as large as previously estimated. In about half of that crustal mass, nuclear matter occurs in shapes very different from the roughly spherical nuclei familiar at lower densities. The thinner crust and the unusual nuclear shape have important consequences for theories of the rotational and thermal evolution of neutron stars, especialy theories of glitches.
We have observed a two-vibron bound-to-unbound transition in solid D2 by Raman scattering at a pressure of 34(2) GPa. We investigated the transition by increasing the vibron bandwidth, through the application of pressure, until it dominated the intramolecular anharmonicity. We present an analysis of a simple Hamiltonian that gives the experimental bivibron binding energy and the critical bandwidth-to-anharmonicity ratio. Our results indicate that while the vibron bandwidth increases markedly with pressure, the anharmonicity remains constant.
It is shown that a fluid flow which are invariant under translations along their vorticity field directions can be described in terms of a formally 2D system. Its nonviscous behavior of the scalar vorticity is governed by Hamiltonian dynamics, similar to the 2D line vortex case. Applying a statistical mechanical method, the equilibrium distribution of the vorticity field for such a general 2D system is shown to obey a nonlinear partial differential equation that is a generalization of the sinh-Poisson equation derived by Montgomery and Joyce (1973, 1974). Thus, if the domain containing the fluid is finite, similar negative temperature states may occur and the distribution of the vorticity intensity may become localized in space. The results are believed to have applications in studying large-scale partial and temporal properties of flows having small but nonzero viscosity. The analysis can probably be extended to other fluid systems with curved magnetic field lines.
Microwave and infrared measurements are reported for the van der Waals complex ArCH3CCH and its isotopomers. The structure is T-shaped with equilibrium center-of-mass separation of 3.73 A and an angle of 82 deg between the molecule symmetry axis and the van der Waals bond. The infrared and microwave spectra are complex due to the effects of a slightly hindered internal rotor. Analysis of the spectral data shows that the dipole moment is almost parallel to the dimer b axis. A modified vibration/rotation Hamiltonian that includes an internal rotor potential is used to show that the barrier to internal rotation is near 10.8/cm.
The millimeter-wave spectrum of the CaH and CaD radicals (X 2Sigma(+)) has been observed in the laboratory via direct absorption spectroscopy. The species were generated by the reaction of calcium vapor, produced in a Broida-type oven, with hydrogen atoms created in a microwave discharge. The six hyperfine components of the N = 0 yields 1 rotational transition of CaH near 254 GHz were resolved and their frequencies determined to an accuracy of +/- 100 kHz. The main hyperfine lines originating in the N = 0 yields 1, 1 yields 2, and 2 yields 3 rotational transitions of CaD were also detected. Spectroscopic constants were determined for both radicals from a nonlinear least squares fit to the data, using a 2Sigma Hamiltonian. These measurements constitute the first laboratory observation of CaH at high spectral resolution, and are essential to the detection of this radical in interstellar space.
The ground state of PtH2 and several low-lying states of PtH(+) and PtH have been studied at the all-electron self-consistent-field level of theory to examine the importance of relativistic effects. The results of calculations based on Dirac-Hartree-Fock theory, nonrelativistic theory, and the spin-free no-pair relativistic approximation of Hess are compared to separate the effects of the spin-free terms and the spin-orbit terms of the Hamiltonian on the relativistic corrections to the molecular properties. Comparison is also made between first-order perturbation theory including the one-electron spin-free terms and the method of Hess to determine the size of effects beyond first order. It is found that the spin-orbit interaction significantly affects the properties and energetics of these molecules because of the participation of the Pt 5d orbitals in the bonding, and that effects beyond first order in perturbation theory are large. Any treatment of Pt compounds will have to include both the spin-free and spin-orbit interactions for an accurate description.
Static-field theoretical studies on molecular second-order polarizabilities (beta) of benzophenone derivatives were performed. Calculations were based on the use of shaped electric fields and semiempirical Hamiltonians. Either an electron-donating (amine) or an electron-withdrawing (nitro) substituent was incorporated into a phenyl ring of benzophenone; the phenyl rings of benzophenone were oriented either coplanar or perpendicular to the carbonyl. The change in charge transfer with respect to the electrophilic character of the carbonyl group was monitored to determine its effect on the molecular second-order polarizability. Calculations were performed for all constitutional isomers of the two benzophenone derivatives.
A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.
The appearance of touch points in state constrained optimal control problems with general vector-valued control is studied. Under the assumption that the Hamiltonian is regular, touch points for first-order state inequalities are shown to exist only under very special conditions. In many cases of practical importance these conditions can be used to exclude touch points a priori without solving an optimal control problem. The results are demonstrated on a simple example.
The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).