For a symmetrical quantum double square well potential, we find analytical expressions satisfied by the quantized energies. Graphical or numerical solutions of the former relations allow us to calculate normalization constants and construct the first eight solutions of the Schrödinger equation. With these exact solutions, we analyze quantum tunneling across a potential barrier and compare our r...

Apparently, the energy levels merge and disappear in many PT symmetric models. This interpretation is incorrect: In square-well model we demonstrate how the doublets of states in question continue to exist at complex conjugate energies in the strongly non-Hermitian regime. PACS 03.65.Fd,03.65.Ge,03.65.Nk

We present an analytical investigation of revival phenomena in the finite square-well potential. The classical motion, revival, and super-revival time scales are derived exactly for wave packets excited in the finite well. These time scales exhibit a richer dependence on wave-packet energy and on potential-well depth than has been found in other quantum systems: They explain, for example, the d...

Both symmetric and symmetry breaking analytic solutions to the one-dimensional nonlinear Schrödinger equation with a double square well potential are known, but not straightforward to obtain numerically. The former generalize solutions to the linear equations, the latter owe their very existence to the nonlinearity. These include, for example, solutions corresponding to the wave function locali...

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envel...

We introduce the idea of an ‘‘equi-g(r) sequence.’’ This consists of a series of equilibrium many-body systems which have different number densities r but share, at a given temperature, the same form of pair correlation function, termed ‘‘target g(r).’’ Each system is defined by a pair potential indexed by r as in ur(r). It is shown that for such a sequence a terminal density r ! exists, beyond...

Accurate virial coefficients B_{N}(λ,ɛ) (where ɛ is the well depth) for the three-dimensional square-well and square-step potentials are calculated for orders N=5-9 and well widths λ=1.1-2.0 using a very fast recursive method. The efficiency of the algorithm is enhanced significantly by exploiting permutation symmetry and by storing integrands for reuse during the calculation. For N=9 the stora...

Cluster integrals are evaluated for the coefficients of the combined temperature- and density-expansion of pressure: Z = 1 + B2(β) η + B3(β) η(2) + B4(β) η(3) + ⋯, where Z is the compressibility factor, η is the packing fraction, and the B(i)(β) coefficients are expanded as a power series in reciprocal temperature, β, about β = 0. The methodology is demonstrated for square-well spheres with λ =...

Fluid-solid phase transition and coexistence of square-well fluids confined in narrow cylindrical hard pores are characterized using molecular simulation methods. The equation of state containing a fluid phase, a solid phase and a fluid-solid coexistence state was separately obtained for different attractive ranges of potential well and pore diameters; lambda=1.2, 1.3, 1.4, and 1.5 for a pore o...

Schrödinger equation with the imaginary, PT symmetric potential V (x) = i x is studied and discussed in momentum representation, via a solvable square-well approximation of its kinetic term.