Showing papers on "Finite potential well published in 1976"
TL;DR: In this paper, it was shown that the singularity acts as an impenetrable barrier if the potential is not integrable up to a singularity, but that the behavior is not essentially different from that of a potential which does not become infinite.
Abstract: In quantum mechanics of one dimension it is shown for potentials which become infinite at a point but are continuous elsewhere, that the singularity acts as an impenetrable barrier if the potential is not integrable up to the singularity, but if the potential is integrable the behavior is not essentially different from that of a potential which does not become infinite.
93 citations
TL;DR: An analytical equation for the Helmholtz free energy of a pure fluid of particles interacting according to a squarewell potential is derived from the Barker-Henderson perturbation theory.
Abstract: An analytical equation for the Helmholtz free energy of a pure fluid of particles interacting according to a square‐well potential is derived from the Barker–Henderson perturbation theory. An analytical treatment of the solution of the Percus–Yevick integral equation for a fluid of hard spheres yields an analytical approximation for the integrals in the terms of the perturbation expansion.
41 citations
TL;DR: In this article, the Riemann function is used to find the conditions for the existence of the kernel of the inverse problem at a fixed value of the angular momentum, where the Coulomb potential is included in the reference potential.
Abstract: Systematic use is made of the Riemann function to find the conditions for the existence of the kernel of the inverse problem at fixed value of the angular momentum. When the reference potential is the centrifugal one, only an l‐dependent condition on the potential must be required in the Marchenko case; in the Gel’fand–Levitan case, the condition is l‐independent. When the Coulomb potential is included in the reference potential, an exponential decrease of the potential is needed in both instances.
27 citations
TL;DR: In this article, the potential energy of interaction between two molecules is expanded in powers of electron interchange using spin-coupled formalism, where space and spin coordinates are explicitly separated, and this leads to compact and systematic expressions for the various terms in the expansion.
Abstract: The potential energy of interaction between two molecules is expanded in powers of electron interchange. The spin-coupled formalism, where space and spin coordinates are explicitly separated, is used and this leads to compact and systematic expressions for the various terms in the expansion. A comprehensive diagram technique is developed with the aid of which any term in the expansion can be obtained by inspection . The range of application of the theory is discussed and it is shown that this approach is particularly suitable for interactions between non-bonded systems whose overlap with each other is always small. For bonded systems, the method is suitable for interactions in the long and intermediate ranges.
17 citations
TL;DR: In this article, an analytical expression for the structure factor of liquid magnesium and cadmium was derived by using a square well potential as a perturbation over the hard sphere potential.
13 citations
TL;DR: In this article, the transcendental equations that determine the bound-state energy eigenvalues of the one-dimensional square well and the s states of the three-dimensional well are cast into a form that can easily be solved to high accuracy on a pocket calculator.
Abstract: The transcendental equations that determine the bound‐state energy eigenvalues of the one‐dimensional square well and the s states of the three‐dimensional well are cast into a form that can easily be solved to high accuracy on a pocket calculator Numerical examples of various one‐dimensional wells and the deuteron are presented
11 citations
TL;DR: In this article, the deuteron stripping reactions are considered and the short-range correlations for the nucleons in the nuclei are taken into account, and the differential cross sections for the two nuclear reactions are calculated for each of the nuclear potential forms.
Abstract: Deuteron stripping reactions are considered. The short-range correlations for the nucleons in the nuclei are taken into account. The neutron- proton nuclear potential in the deuteron is taken as a long-range attractive potential surrounded by a short-range repulsive potential. We take different forms for the two parts of the neutron-proton nuclear potential. The differential cross sections for the two nuclear reactions $sup 28$Si(d,p)$sup 29$Si and $sup 40$Ca(d,p)$sup 41$Ca have been calculated for each of the nuclear potential forms. Fitting our theoretical calculations, using the distorted-wave Born approximation, with the experimental data yields good agreement. The more reliable spectroscopic factors for these reactions have been extracted. (AIP)
9 citations
TL;DR: In this article, an off-shell momentum (or several offshell momenta) is introduced to find points where the phase shift has an extreme value, at which the matrix Pade approximants are extraordinarily accurate.
Abstract: In calculations using matrix Pade approximants, an off-shell momentum (or several off-shell momenta) is introduced. In previous work, this momentum was chosen arbitrarily and not varied. However, it is a variational parameter and may be varied to find points where the phase shift has an extreme value. At such points, the matrix Pade approximants are extraordinarily accurate, even for potentials with strong repulsive cores. (AIP)
8 citations
01 Dec 1976
TL;DR: In this paper, the three dimensional square well potential is discussed and it is shown that there are no observable resonances in the cross section except for the zero energy resonance, which is remarkable because almost every textbook on the topic discusses a series of regularly spaceds wave resonances.
Abstract: The three dimensional square well potential is discussed. It is shown that there are no observable resonances in the cross section except for the zero energy resonance. This is remarkable because almost every textbook on the topic discusses a series of regularly spaceds wave resonances. The lack of non-zero energy resonances in thes wave cross section of the square well potential cannot, however, be generalized to other purely attractive potentials. This is shown with a specific example.
6 citations
TL;DR: In this paper, a meson-theoretic model of the intermediate range nucleon-nucleon potential is presented with emphasis placed on the two-pion exchange contribution.
5 citations
TL;DR: In this paper, a model calculation of the absorption bandwidth of radical anions of some circular hydrocarbons was carried out for one-election bound-free transitions in a cylindrical square well potential.
TL;DR: In this article, a general expression for the surface Green function at the interface of arbitrary shape between two media is derived by matching the Green functions and applied to the spherical square well potential.
Abstract: A general expression for the surface Green function at the interface of arbitrary shape between two media is derived by matching the Green functions. The result is applied to the spherical square well potential.