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Finite potential well

About: Finite potential well is a research topic. Over the lifetime, 672 publications have been published within this topic receiving 10852 citations.


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TL;DR: In this paper, the equation of state for a fluid of molecules interacting according to the square-well potential is evaluated by treating the attractive potential as a perturbation on the hard-sphere potential.
Abstract: The equation of state for a fluid of molecules interacting according to the square‐well potential is evaluated by treating the attractive potential as a perturbation on the hard‐sphere potential. This leads to an expansion in inverse powers of the temperature. The first‐order term is evaluated exactly (except for the approximation of using the Percus—Yevick expression for the hard‐sphere radial distribution function). Two slightly different approximations for the second‐order term are given and shown to lead to similar results. With first‐and second‐order terms included, the calculated equation of state is in excellent agreement with quasiexperimental Monte Carlo and molecular‐dynamics results at all temperatures including the lowest temperatures for which such calculations have been made, far below the critical temperature and at liquid densities. The reasons for this good agreement, particularly at high densities, are discussed in terms of a novel formulation of the perturbation theory, and the implications of the results for fluids with more realistic potential functions are considered.

983 citations

Journal ArticleDOI
TL;DR: In this article, the transmission coefficients T l and total reaction cross section σ R for alpha particles in the energy range 0-46 MeV interacting with 20 target nuclei with atomic numbers ranging from 10 to 92 are calculated with an optical model program in which a previously determined complex nuclear potential is utilized.

305 citations

Journal ArticleDOI
TL;DR: In this article, the fractional Schrodinger equation was solved for a free particle and for an infinite square potential well, and the energy levels and the normalized wave functions of a particle in a potential well were obtained.
Abstract: The fractional Schrodinger equation is solved for a free particle and for an infinite square potential well. The fundamental solution of the Cauchy problem for a free particle, the energy levels and the normalized wave functions of a particle in a potential well are obtained. In the barrier penetration problem, the reflection coefficient and transmission coefficient of a particle from a rectangular potential wall is determined. In the quantum scattering problem, according to the fractional Schrodinger equation, the Green’s function of the Lippmann-Schwinger integral equation is given.

231 citations

Journal ArticleDOI
TL;DR: In this paper, the shape of the coexistence curve of the square-well fluid with short potential range is nearly cubic and the critical density ρc=0.070±0.005, both in reduced units.
Abstract: Coexistence curves of square-well fluids with variable interaction width and of the restricted primitive model for ionic solutions have been investigated by means of grand canonical Monte Carlo simulations aided by histogram reweighting and multicanonical sampling techniques. It is demonstrated that this approach results in efficient data collection. The shape of the coexistence curve of the square-well fluid with short potential range is nearly cubic. In contrast, for a system with a longer potential range, the coexistence curve closely resembles a parabola, except near the critical point. The critical compressibility factor for the square-well fluids increases with increasing range. The critical behavior of the restricted primitive model was found to be consistent with the Ising universality class. The critical temperature was obtained as Tc=0.0490±0.0003 and the critical density ρc=0.070±0.005, both in reduced units. The critical temperature estimate is consistent with the recent calculation of Caillol...

219 citations

Journal ArticleDOI
TL;DR: In this paper, a simple yet exact method of solving the Schrodinger equation across an arbitrary one-dimensional piecewise linear potential is described, where the solution can be expressed as a linear combination of the Airy functions.
Abstract: A simple yet exact method of solving the Schrodinger equation across an arbitrary one‐dimensional piecewise‐linear potential is described. It is based on the analytical solution of the Schrodinger equation across a linear potential, where the solution can be expressed as a linear combination of the Airy functions. Proper boundary conditions are imposed at the interface between adjacent linear intervals of the potential, and a transfer‐matrix procedure is utilized in the derivation. The quantum mechanical transmission coefficient across a potential barrier and eigenenergies of a potential well can also be easily calculated using this method.

192 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20225
20217
202014
20198
20187
201719