Showing papers on "Finite potential well published in 1972"

Effects of an Attractive Well Potential on the Atom–Diatomic Molecule Collinear Collision

Abstract: The effect on the vibrational transition probability of an attractive well in the interaction potential for the collinear collision of an atom with a diatomic oscillator is investigated. Two forms of the potential are considered. For a square barrier potential, a square well introduces sharp resonances in the transition probability. It is shown that the position of these resonances may be predicted by a simple formula. For a ``soft'' Morse interaction potential no resonances are observed. It is shown in this case that the transition probability is determined more by the slope of the potential at the classical turning point than by the presence or absence of an attractive well.

Physical interpretation of glory undulations in scattering cross sections.

Abstract: The relation between glory undulations and the detailed nature of the potential energy of interaction of two molecules having a minimum containing one or more bound states is clarified, i.e., a physical interpretation is given to the undulations. Although the number, amplitude, and spacing of the oscillations all give information about the potential, the spacing is most often used because it can be most accurately measured. Results are given which show fairly explicitly just what information on the interaction potential is contained in the spacing of the glory oscillations. Glory oscillations put strong known constraints on any potential model.

Square‐Well Potential. I. An Yvon‐Born‐Green Square‐Well Equation of State

Abstract: The Yvon‐Born‐Green integral equation for the pair correlation function is solved for the square‐well potential with σ2/σ1=185, using a θ=e/kT expansion scheme previously devised by Kirkwood et al The pertinent results are expressed in a power series of density by a least squares technique for the entire gas and liquid regimes The coexistence region is determined, including the location of the critical point, and thermodynamic properties are calculated and tabulated as functions of state The validity and utility of the results are examined in detail

Solutions of the Relativistic Two-Body Problem. II. Quantum Mechanics

Abstract: This paper discusses the formulation of a quantum mechanical equivalent of the relative time classical theory proposed in Part I. The relativistic wavefunction is derived and a covariant addition theorem is put forward which allows a covariant scattering theory to be established. The free particle eigenfunctions that are given are found not to be plane waves. A covariant partial wave analysis is also given. A means is described of converting wavefunctions that yield probability densities in 4-space to ones that yield the 3-space equivalents. Bound states are considered and covariant analogues of the Coulomb potential, harmonic oscillator potential, inverse cube law of force, square well potential, and two-body fermion interactions are discussed.

A new impurity calculation

Abstract: A new Green function technique to solve the Schrodinger equation in two media joined on a surface is applied to a square well potential in a free-electron gas. The method gives both the bound states and the change in charge density and density of states.

Square‐Well Potential. III. Transport Properties of Liquids

Abstract: The Davis‐Rice‐Sengers square‐well theory of transport for simple dense gases and liquids is tested with Yvon‐Born‐Green theoretical pair correlation functions for σ2/σ1=1.85. Comparison with experiment shows that the theory correctly predicts the qualitative features of liquid argon transport properties and quantitatively is very good at high temperatures and densities in the liquid region. An adjustment of intermolecular potential parameters is shown to improve the predictions of the theory uniformly. Some comments are made concerning the success of this theory in light of recent studies of the Rice‐Allnatt theory.

Computer Solutions to a Realistic “One-Dimensional” Schrödinger Equation

Abstract: An important technique for teaching introductory wave mechanics is provided by the numerical calculation of stationary state solutions of the Schrodinger equation. Realistic problems in wave mechanics that do not require sophisticated computer techniques are very valuable for the instruction of undergraduates. In the central-field model for atoms, the calculation of electron states reduces to the solution of a one-dimensional differential equation whose numerical solutions are no more difficult to obtain than those for a finite square well. A method used by our students is discussed in this paper for the calculation of the electron wavefunctions in a central-field potential. By working this problem, students obtain meaningful results that give them insight into the theory of atomic structure. Results of their experience are included, and possibilities of extending this example are discussed.

Even and Odd Spectra of One-Dimensional Symmetrical Potential. II. Dirac Theory

Abstract: The discrete spectrum of a one-dimensional symmetrical potential is studied within the framework of the Dirac theory and compared to the Schrodinger spectrum, using the variable phase approach. Separate Riccati equations characterizing the even and odd spectra are given, and transcendental inequalities yield energy bounds on the two lower states. Conditions sufficient to support one odd state are established, and some numerical results are checked for a square well potential.