Geoffrey Hunter

Rotation-vibration level energies of the hydrogen and deuterium molecule-ions

Bound and quasi-bound rotation-vibration level energies, calculated in the adiabatic approximation, are tabulated for H 2 + and D 2 + together with the resonance widths of the less stable quasibound states. Bound levels for HD + , calculated from a single adiabatic internuclear potential, are also listed, together with an estimate of their likely range of validity. Expectation values for the internuclear separations are also presented, graphically.

Proton collisions with hydrogen atoms at low energies: quantum theory and integrated cross-sections

Cross-sections for collisions of protons with hydrogen atoms have been computed by partial wave analysis within the perturbed stationary state theory. Phase shifts with 6 decimal accuracy were obtained by the use of adiabatically corrected 1Sσg and 2Pσu H+2 potentials together with accurate numerical methods. The phase shifts and the integrated cross-sections derived from them are reported for 57 values of the energy ranging from 0.0001 eV (1.2 K) to 10 eV. These accurate quantum mechanical results differ from semi-classical results especially at energies below 0.1 eV.

The Exact Schrödinger Equation for the Electron Density

The Schrodinger equation satisfied by the square root of the electron density is derived without approximation from the theory of marginal and conditional amplitudes. The equation arises from a factorization of the total N—electron wavefunction defined by the normalisation appropriate to a conditional amplitude. The effective potential is, in contrast to that in the one—electron Dyson equation, a scalar, local potential that only depends upon one stationary state of the N—electron system. The equation is easily transformed into an exact differential equation for the electron density itself; the transformation leaves the potential energy and the energy eigenvalue unchanged. In this exact equation the kinetic energy is identical with the kinetic energy in the Thomas-Fermi-Weizsacker differential equation. The exact equation applies to excited states as well as to the ground state, thus extending the Hohenberg-Kohn density-functional theorem to excited states. The exact equation provides a basis for self-consistent-density calculations. This Schrodinger equation is an exact dynamical model for computing effective one-electron potentials from known N—electron wavefunctions, or from experimental electron densities. Two forms of the theory are presented: 1) the static nuclei model pertinent to theoretical calculations within the Born-Oppenheimer separation, and 2) the non-Born-Oppenheimer (vibrationally averaged) model appropriate to computation of the effective one-electron potential from experimental electron densities.

Scattering of protons by hydrogen atoms at low energies: Phase shifts and differential cross sections

Phase shifts and differential cross sections for spin exchange (charge transfer) and total elastic scattering of protons by hydrogen atoms are presented for 36 and 38 values, respectively, of the collisional kinetic energy in the range 0.0001 to 10 eV (center of mass). The phase shifts are tabulated with a precision of six decimal digits. Each cross section is presented as a graph covering the complete angular range from 0 to ..pi.. radians (in center-of-mass coordinates). The phase shifts were obtained via partial wave analysis within a modified Perturbed-Stationary-States theory by calculations based upon very accurate (nonrelativistic) internuclear potential energies for the 1 Ssigma/sub g/ and 2Psigma/sub u/ electronic states of H/sub 2//sup +/. The cross sections demonstrate a transition from purely quantum behavior at very low energies ( 1 eV) in which protons scattered by spin exchange are angularly separated from those scattered without exchange. Thus the in-principle unobservable charge-transfer cross section becomes physically measurable at energies greater than about 1 eV.

The scattering states of HD

Elastic and charge-transfer cross-sections for collisions of protons (or deuterons) with deuterium (or hydrogen) atoms have been calculated for 31 values of the energy from 0.001 to 7.5 eV. They were obtained by a fully quantum mechanical method. The internuclear potentials obtained from the Born-Oppenheimer separation were improved by the addition of the first order corrections for nuclear motion, and accurate phase shifts were obtained by numerical solution of a pair of coupled radial Schrödinger equations. The cross-sections are compared with experimental and theoretical values obtained previously.

Asymptotic expansions of mathieu functions in wave mechanics

Abstract Solutions of the radial Schrodinger equation containing a polarisation potential r −4 are expanded in a form appropriate for large values of r . These expansions of the Mathieu Functions are used in association with the numerical solution of the Schrodinger equation, to impose the asymptotic boundary condition in the case of bound states, and to extract phase shifts in the case of scattering states.

Einstein’s Photon Concept Quantified by the Bohr Model of the Photon

The photon is modeled as a monochromatic solution of Maxwell’s equations confined as a soliton wave by the principle of causality of special relativity. The soliton travels rectilinearly at the speed of light. The solution can represent any of the known polarization (spin) states of the photon. For circularly polarized states the soliton’s envelope is a circular ellipsoid whose length is the observed wavelength (λ), and whose diameter is λ/π; this envelope contains the electromagnetic energy of the wave (hv = hc/λ). The predicted size and shape is confirmed by experimental measurements: of the sub‐picosecond time delay of the photo‐electric effect, of the attenuation of undiffracted transmission through slits narrower than the soliton’s diameter of λ/π, and by the threshold intensity required for the onset of multiphoton absorption in focussed laser beams. Inside the envelope the wave’s amplitude increases linearly with the radial distance from the axis of propagation, being zero on the axis. Outside the ...

Electrons and Photons as Soliton-Waves

Whether the physical world is composed of indivisible atoms, or alternatively is an infinitely divisible continuum, is a question that has concerned natural philosophers for hundreds of years; specifically Newton speculated about whether light is composed of a stream of particles or is a wave motion within some underlying medium (the “ether”).

Hermitian operators for two-centre wavefunctions

Semi-analytical solutions of the Schrödinger equation for a particle moving in the electrostatic field of two other particles a fixed distance apart, are derived in such a way that the resulting matrix eigenvalue equations contain real symmetric band matrices. Numerical techniques appropriate to the solution of the two simultaneous matrix eigenvalue equations are described; in particular the bisection method is used to determine precisely the significant truncation order of the matrices for a given numerical precision.

The nature of the B(3) field

Abstract The nature of the B (3) field is determined through deductions from its mathematical definition; B (3) is a vector function of the magnetic field of electromagnetic radiation. The sign and magnitude of B (3) measure the polarization of the radiation, and it is re-normalized to define the Polarization Index (a dimensionless number of magnitude unity), which proves to be identical with one of Stokess parameters. This is revealed to be the essential nature of the B (3) field. The definition of B (3) (and of the Polarization Index) is generalized in terms of all components of the electromagnetic field rather than only the transverse magnetic components. The analysis leads to internal inconsistencies if the B (3) field is presumed to be the longitudinal component of the physical magnetic field of electromagnetic radiation as asserted by M.W. Evans (the originator of the theory of the B (3) field). This inference explains the failure of experimental investigations to detect the hypothetical longitudinal magnetic field of radiation. It also corroborates a disproof by counter-example by E. Comay.