Jiro Ozaki

Monte Carlo Solutions of Schrödinger's Equation for H+2 Ion in Strong Magnetic Fields

The analytical expressions suitable for the Monte Carlo calculation to obtain the solution of Schrodingers equation of hydrogen molecular ion in a strong magnetic field are derived. The wave functions, the energy values and the equilibrium internuclear distances of 1σ g state of H + 2 are obtained numericallly through the Monte Carlo simulation and compared with other results based on the variational method. The agreement between them is fairly good over a wide range of magnetic field. The calculation of the energy values of 1π g state of H + 2 for various internuclear distances taking a constant magnetic field as a parameter, shows that the antibonding 1π g state in the absence of the external magnetic field changes to a bonding state with an increasing magnetic field. The lowest energy values and the equilibrium internuclear distances of 1π g state are also calculated for various magnetic field.

Energies of the H+2 ion in strong magnetic fields

Abstract Variational calculations of the energy values and the equilibrium internuclear separations of the H+2 ion in the 1σg and 1πg states are carried out to confirm our previous results based on the Monte Carlo method; in the absence of an external magnetic field the antibonding 1πg state changes to a bonding state with increasing magnetic field. As a byproduct, a simple variational form is proposed for the wave function of the H atom in strong magnetic fields.

Energies of the H2+ Ion in Strong Magnetic Fields: Variational Adiabatic Method

By using the variational adiabatic method, the energy values and the equilibrium internuclear separations of the H 2 + ion in π g state in strong magnetic fields are calculated and compared with those obtained from the adiabatic method and the Monte Carlo method and our conclusion through the Monte Carlo Method are confirmed, that is, the antibonding state π g in the absence of external magnetic field changes to a bonding state with an increasing magnetic field.

Solution of the Temperature-Dependent Thomas-Fermi-Dirac-Weizsäcker Equation with a Correlation Correction

The temperature-dependent Thomas-Fermi-Dirac-Weizsacker theory with a correlation correction, which was proposed previously (J. Phys. Soc. Jpn. 54 (1985) 1282), is applied to an atom embedded in a neutral heat bath. Taking Fe atom as an example, the electron density, energy, free energy, pressure, and entropy are evaluated over a wide range of temperature and compression (0≦ k T ≦1000 eV, 0.1≦ρ/ρ 0 ≦1000). These are compared with the results obtained from the simple Thomas-Fermi Theory and the Thomas-Fermi-Dirac theory with the correlation correction. The effect of the exchange-correlation correction and that of the Weizsacker correction are discussed.

A Remark on the Monte-Carlo Solution of the Schrödinger Equation for Molecular Systems

The Grimm-Storers Monte-Carlo method based on the Feynman path integral and the Andersons one based on the diffusion equation are reformulated to clarify their similarities from computational standpoint irrespective of the quite different consideration process. The comparison of these two methods indicates the limitation of the accuracy and the applicability of Monte-Carlo method. Numerical results on H atom and H + 3 ion are presented as illustrative examples.

Periodic Orbits of Henon Heiles Hamiltonian --Bifurcation Phenomenon--

In this paper we discuss the bifurcation of periodic orbits for the Henon-Heiles Hamiltonian. The model of Henon-Heiles> has been studied by many authors since 1964. We make no attempt to list all references to periodic orbits of this Hamiltonian, but only those which are representative in the field of celestial mechanics,> dynamical systems,> and solid state physics.> El-Sabaa and Sherief> discussed nine classes of the main periodic orbits in Henon-Heiles potential which they regarded as a two-dimensional galactic potential. Davies et al.> studied eight families, using the monodromy method, of the simple and basic orbits in Henon-Heiles potential partly on the basis of Churchill et al.s study> where the periodic orbits in Henon-Heiles potential were classified into the eight families taking into account various symmetries. Other literature cited for periodic orbits of Henon-Heiles Hamiltonian can be found, for references in the past 15 years, in Ref. 3), and for earlier references in Ref. 5). Akhiezer et al. > studied, in their research of dynamical chaos of charged particles in a crystal, the dynamical chaos of the Henon-Heiles hamiltonian, regarding Henon-Heiles potential, on the basis of a reasonable theory, as a model potential of the real channel potentials in a crystal. Bifurcation theory has been developed by many authors since the time of Poincare. Meyer> analytically studied the bifurcation of periodic orbits for a conservative differential equation, Duffing equation, selecting from these many bifurcation theories those cases which are generic. Aguiar et al.7l extended Meyers work, in which he confined himself to the generic case of a Hamiltonian without symmetry, to include Hamiltonian with time-reversal symmetry and space-reflection symmetry. That is, Aguiar et al.7l developed a method to study the nongeneric case of a Hamiltonian with symmetries, beyond the generic case of a Hamiltonian without symmetry. Generally speaking, some of typical types of generic bifurcations are influenced directly by special symmetries of the system. All Hamiltonian systems discussed below are of the form

Monte Carlo solution of Schrödinger's equation for the hydrogen atom in a magnetic field

Abstract The analytical expressions suitable for the Monte Carlo calculation to obtain the solution of Schrodingers equation of the hydrogen atom in a magnetic field are developed. The energy values and the wavefunctions for the even states of m = 0 and 1 are obtained numerically and compared with other results based on the variational method. The agreement between them is rather good.

Adiabatic Potentials of H+2 Ion in Strong Magnetic Fields

We have calculated, from the adiabatic potentials, the total energies and the equilibrium internuclear separations of H 2 + ion in antibonding states δ u , φ g , γ u , and η g as well as bonding states δ g , φ u , γ g , and η u in strong magnetic fields. The adiabatic potentials of H 2 + in antibonding states have the minimum when the magnetic field is strong. This means magnetic field stasbilizes dissociative H 2 + . With regard to the bonding states, our results reproduce those by M. Vincke and D. Baye [J. Phys. B: At. Mol. Phys. 18 (1985) 167] which are considered to be the most reliable.

The change in character of the even z-parity states from antibonding to bonding in the H+2 ion by strong magnetic fields

Abstract Using an adiabatic method, the total energies and equilibrium internuclear separations of the even z -parity states δ g , φ u , γ g , and η u of a H + 2 ion in strong magnetic fields ≈ 2.35 × 10 8 T are calculated. It is concluded that any even z -parity state of the H + 2 ion will become the corresponding stronger bonding state with increase of magnetic field strength, even if it is originally in an antibonding state at zero magnetic field.