We find supersymmetric partners of a family self-adjoint operators which are extensions the differential operator −d2/dx2 on L2[−a,a], a>0, that is, one dimensional infinite square well. First all, we classify these in terms several choices parameters determining each extensions. There essentially two big groups In one, ground state has strictly positive energy. On other, either zero or nega...

The thermodynamic functions for square-well gases evaluated till the third virial coefficient are investigated at an isobaric process. Some thermodynamic functions are analytically expressed as functions of intensive variables, temperature, and pressure. Some thermodynamic quantities for H2O are calculated numerically and drawn graphically. In critical states, the heat capacity, thermal expansi...

Various Monte Carlo techniques are used to determine the complete phase diagrams of the square-well model for the attractive ranges lambda = 1.15 and lambda = 1.25. The results for the latter case are in agreement with earlier Monte Carlo simulations for the fluid-fluid coexistence curve and yield new results for the liquidus-solidus lines. Our results for lambda = 1.15 are new. We find that th...

The PT-symmetric square well problem is considered in a SUSY framework when the coupling strength lies below the critical value where PT symmetry becomes spontaneously broken. We find SUSY partner potentials to exist admitting a hierarchy with energy levels depicting an unbroken SUSY situation. Such a hierarchy is a PT-symmetric analogue of the family of sec2-like potentials, to which it reduce...

Using kinetic Monte Carlo simulation, we model gas-liquid spinodal decomposition in a size-polydisperse square well fluid, representing a "near-monodisperse" colloidal dispersion. We find that fractionation (demixing) of particle sizes between the phases begins asserting itself shortly after the onset of phase ordering. Strikingly, the direction of size fractionation can be reversed by a seemin...

We examine the classical problem of an infinite square well by considering Hamilton’s equations in one dimension and Hamilton-Jacobi equation for motion in two dimensions. We illustrate, by means of suitable examples, the nature of the periodic motion of a particle trapped inside the well. E-mail address: [email protected] Directeur de recherches FNRS; E-mail address: [email protected]

Recently, a class of PT -invariant quantum mechanical models described by the nonHermitian HamiltonianH = p2 + x2(ix) was studied. It was found that the energy levels for this theory are real for all > 0. Here, the limit as →∞ is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, H = p2 + x2M(ix) (M = 1, 2, 3, . . .) is also stud...

We investigate the ability of the reference hypernetted-chain integral equation to describe the phase diagram of square-well fluids with four different ranges of attraction. Comparison of our results with simulation data shows that the theory is able to reproduce with fairly good accuracy a significant part of the coexistence curve, provided an extrapolation procedure is used to circumvent the ...

The quantum dynamics of the periodically-driven infinite square well is examined. This simple system illustrates some important aspects of quantum chaos. The phase space structure of the quantum eigenstates are shown to mimic the structure of the classical phase space and these eigenstates show a transition from “regular” to “chaotic” as the strength of the driving field is increased. The spaci...

A Born–Green–Yvon integral equation approach is used to study the structure and phase behavior of a fluid of fused square-well-sphere dimers. We compute site–site distribution functions for dimers with bond lengths of L50.6s , 0.8s, and 1.0s ~where s is the hard-sphere diameter! and square-well diameters ranging from l51.25s to 2.0s over a wide range of temperature and density, and make compari...