Showing papers on "Finite potential well published in 2010"

Hydrostatic pressure and conduction band non-parabolicity effects on the impurity binding energy in a spherical quantum dot

Abstract: The binding energy of a shallow hydrogenic impurity in a spherical quantum dot under hydrostatic pressure with square well potential is calculated using a variational approach within the effective mass approximation. The effect of conduction band non-parabolicity on these energies is also estimated. The binding energy is computed for GaAs spherical quantum dot as a function of dot size, hydrostatic pressure both in the presence and absence of the band non-parabolicity effect. Our results show that (i) the hydrostatic pressure increases the impurity binding energy when dot radius increases for a given pressure, (ii) the hydrostatic pressure with the band non-parabolicity effect effectively increases the binding energy such that the variation is large for smaller dots and (iii) the maximum contribution by the non-parabolicity effect is about 15% for narrow dots. Our results are in good agreement with Perez-Merchancano et al. [J. Phys. Condens. Matter 19 (2007) 026225] who have not considered the conduction band non-parabolicity effect.

Use of Equivalent Hermitian Hamiltonian for $PT$-Symmetric Sinusoidal Optical Lattices

Abstract: We show how the band structure and beam dynamics of non-Hermitian $PT$-symmetric sinusoidal optical lattices can be approached from the point of view of the equivalent Hermitian problem, obtained by an analytic continuation in the transverse spatial variable $x$. In this latter problem the eigenvalue equation reduces to the Mathieu equation, whose eigenfunctions and properties have been well studied. That being the case, the beam propagation, which parallels the time-development of the wave-function in quantum mechanics, can be calculated using the equivalent of the method of stationary states. We also discuss a model potential that interpolates between a sinusoidal and periodic square well potential, showing that some of the striking properties of the sinusoidal potential, in particular birefringence, become much less prominent as one goes away from the sinusoidal case.

A spherical model with directional interactions: II. Dynamics and landscape properties

Abstract: We study a binary non-additive hard-sphere mixture with square well interactions only between dissimilar particles. An appropriate choice of the inter-particle potential parameters favors the formation of equilibrium structures with tetrahedral ordering (Zaccarelli et al 2007 J. Chem. Phys. 127 174501). By performing extensive event-driven molecular dynamics simulations, we monitor the dynamics of the system, locating the iso-diffusivity lines in the phase diagram, and discuss their location with respect to the gas-liquid phase separation. We observe the formation of an ideal gel which continuously crosses towards an attractive glass upon increasing the density. Moreover, we evaluate the statistical properties of the potential energy landscape for this model. We find that the configurational entropy, for densities within the optimal network-forming region, is finite even in the ground state and obeys a logarithmic dependence on the energy.

On the low energy behavior of Regge poles

Abstract: We investigate the behavior of Regge poles in the low energy limit. With the use of small argument asymptotics of the spherical Hankel functions, we show that for a finite square well potential, the associated Regge poles tend to the spectral points of the limiting self-adjoint problem. This is generalized to a compactly supported potential by applying a resolvent argument to the difference of the nonzero and zero energy wavefunctions. Furthermore, by an integral equation method we prove analogous results for a potential such that |(1+r)U(r)| is integrable. This confirms the experimental results which show that Regge poles formed during low energy electron elastic scattering become stable bound states.

Effects of hydrostatic pressure and polaronic effects on the correlation energies in a spherical quantum dot

Abstract: The correlation energies in a singlet and in a triplet state of a two-electron quantum dot in a finite barrier square well potential are computed. Closed analytical expressions are obtained in the perturbation method. Effects of band non-parabolicity and polaronic correction are included. Effects of hydrostatic pressure on the correlation energies are computed. Our results show that (i) the correlation energies in the triplet state are negative, reflecting the exchange interaction, (ii) both the singlet and triplet state correlation energies approach zero as the dot size approaches infinity, (iii) while the band non-parabolicity and the polaronic effects are not significant in the estimation of correlation energies, they however decrease the total confined energies to a maximum of 43% in the triplet state, and (iv) the hydrostatic pressure affects the confined energies appreciably for narrow dots only. The interesting cross-over behavior of the triplet and the singlet state energies at a particular dot radius is explained physically.

s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions

Abstract: We examine the zero-range limit of the finite square well in arbitrary dimensions through a systematic analysis of the reduced, s-wave, two-body, time-independent Schrodinger equation. A natural consequence of our investigation is the requirement of a delta function multiplied by a regularization operator to model the zero-range limit of the finite-square well when the dimensionality is greater than one. The case of two dimensions turns out to be surprisingly subtle, and needs to be treated separately from all other dimensions.

Generalized Einstein relation in tilted periodic potential: a semiclassical approach.

Abstract: This paper concerns the investigation of the quantum motion of a system in a dissipative Ohmic heat bath in the presence of an external field using the traditional system-reservoir model. Using physically motivated initial conditions, we then obtain the c-number of the generalized quantum Langevin equation by which we calculate the quantum correction terms using a perturbation technique. As a result of this, one can apply a classical differential equation-based approach to consider quantum diffusion in a tilted periodic potential, and thus our approach is easy to use. We use our expression to calculate the Einstein relation for the quantum Brownian particle in a ratchet-type potential in a very simple closed analytical form using a suitable and convenient approximation. It is found that the diffusion rate is independent of the detailed form of the potential both in quantum and classical regimes, which is the main essence of this work.

s-wave scattering and the zero-range limit of the finite square well in arbitrary dimensions

Abstract: We examine the zero-range limit of the finite square well in arbitrary dimensions through a systematic analysis of the reduced, s-wave two-body time-independent Schr\"odinger equation. A natural consequence of our investigation is the requirement of a delta-function multiplied by a regularization operator to model the zero-range limit of the finite-square well when the dimensionality is greater than one. The case of two dimensions turns out to be surprisingly subtle, and needs to be treated separately from all other dimensions.

Statistics of a Free Single Quantum Particle at a Finite Temperature

Abstract: We present a model to study the statistics of a single structureless quantum particle freely moving in a space at a finite temperature. It is shown that the quantum particle, in response to the temperature, can exchange energy with its environment in the form of heat transfer. The underlying mechanism is diffraction at the edge of the wavefront of its matter wave. The expressions of energy and entropy of the particle are obtained for the irreversible process.

Stringent verification of third order + second order perturbation density function theory: based on short-range square well potential

Abstract: A recently proposed third order + second order perturbation density functional theory (DFT) approach is made self-contained by using a virial pressure from the Ornstein–Zernike integral equation theory as input to determine the numerical value of an associated physical parameter. An exacting examination is formulated by applying the self-contained perturbation DFT approach to a short-range square well fluid of low temperatures subject to various external fields and comparing the theoretical results for density profiles to the corresponding grand canonical ensemble Monte Carlo simulation results. The comparison seems favorable for the third order + second order perturbation DFT approach as a self-contained and accurate predictive approach. It is surprisingly found that this self-contained third order + second order perturbation DFT approach is displayed outstandingly even if a deep SW perturbation term is being accounted for by a second order perturbation expansion. A discussion is presented about potential opportunity for this perturbation scheme.

On the bound-state spectrum of a nonrelativistic particle in the background of a short-ranged linear potential

Abstract: The nonrelativistic problem of a particle immersed in a triangular potential well, set forth by N. A. Rao and B. A. Kagali, is revised. It is shown that these researchers misunderstood the full meaning of the potential and obtained a wrong quantization condition. By exploring the space inversion symmetry, this work presents the correct solution to this problem with potential applications in electronics in a simple and transparent way. c

Poço quadrado quântico finito e método de fatorização

Abstract: The system consisting of a particle subject to a quantum finite square well potential is extensively explored in initial studies of quantum mechanics and it is shown to be quite useful in describing confined systems. In this article we present an alternative way, through the Factorization Method, for determining the eigenfunctions and the energy eigenvalues for the system.

Calculation of eta-meson-nucleus quasibound states with optical potentials of the square-well and woods-saxon forms

Abstract: The results obtained by calculating bound states of eta mesons and nuclei by using a squarewell optical potential are compared with their counterparts based on the use of an optical potential in the Woods-Saxon form. For any reasonable choice of range for a potential that has a sharp boundary, the results for the case of a diffuse boundary demonstrate the need for a greater baryon charge in order that an eta meson form a bound state with nuclei. The dependence of the probability for the formation of etamesonic nuclei on the diffuseness parameter of the optical potential involving the Woods-Saxon radial dependence is revealed.

Effective polar potential in the central force Schrödinger equation

Abstract: The angular part of the Schrodinger equation for a central potential is brought to the one-dimensional 'Schrodinger form' where one has a kinetic energy plus potential energy terms. The resulting polar potential is seen to be a family of potentials characterized by the square of the magnetic quantum number m. It is demonstrated that this potential can be viewed as a confining potential that attempts to confine the particle to the xy-plane, with a strength that increases with increasing m. Linking the solutions of the equation to the conventional solutions of the angular equation, i.e. the associated Legendre functions, we show that the variation in the spatial distribution of the latter for different values of the orbital angular quantum number l can be viewed as being a result of 'squeezing' with different strengths by the introduced 'polar potential'.