scholarly journals Solution of the Schrödinger equation for quantum-dot lattices with Coulomb interaction between the dots

2000 ◽  
Vol 62 (12) ◽  
pp. 8126-8136 ◽  
Author(s):  
M. Taut
Keyword(s):  
Quantum Dot ◽  
Schrödinger Equation ◽  
Coulomb Interaction ◽  
Schrodinger Equation

Bound state solution of the Schrodinger equation for the Woods–Saxon potential plus coulomb interaction by Nikiforov–Uvarov and supersymmetric quantum mechanics methods

2021 ◽  
pp. 2150023
Author(s):  
Enayatolah Yazdankish
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Interaction ◽  
Schrodinger Equation ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Repulsive Interaction ◽  
Saxon Potential ◽  
Special Cases ◽  
Supersymmetry Quantum Mechanics

The generalized Woods–Saxon potential plus repulsive Coulomb interaction is considered in this work. The supersymmetry quantum mechanics method is used to get the energy spectrum of Schrodinger equation and also the Nikiforov–Uvarov approach is employed to solve analytically the Schrodinger equation in the framework of quantum mechanics. The potentials with centrifugal term include both exponential and radial terms, hence, the Pekeris approximation is considered to approximate the radial terms. By using the step-by-step Nikiforov–Uvarov method, the energy eigenvalue and wave function are obtained analytically. After that, the spectrum of energy is obtained by the supersymmetry quantum mechanics method. The energy eigenvalues obtained from each method are the same. Then in special cases, the results are compared with former result and a full agreement is observed. In the [Formula: see text]-state, the standard Woods–Saxon potential has no bound state, but with Coulomb repulsive interaction, it may have bound state for zero angular momentum.

Simple method to incorporate nonparabolicity effects in the Schrödinger equation of a quantum dot

2007 ◽  
Vol 101 (9) ◽  
pp. 093715 ◽  
Author(s):  
F. M. Gómez-Campos ◽  
S. Rodríguez-Bolívar ◽  
J. E. Carceller
Keyword(s):  
Quantum Dot ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Simple Method

Parabolic band approximation of the electron energy levels in a tetrahedral-shaped quantum dot

2008 ◽  
Vol 86 (11) ◽  
pp. 1327-1331
Author(s):  
T Pengpan ◽  
C Daengngam
Keyword(s):  
Quantum Dot ◽  
Schrödinger Equation ◽  
Effective Mass ◽  
Electron Energy ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Nonlinear Schrodinger Equation ◽  
Gradient Term ◽  
Nonlinear Schrödinger

In more elaborate schemes, an electron’s effective mass in a heterostructure semiconductor quantum dot (QD) depends on both its position and its energy. However, the electron’s effective mass can be simply modeled by a parabolic band approximation — the electron’s effective mass inside the QD — which is assumed to be constant and differs from the one outside the QD, which is also assumed to be constant. The governing equation to be solved for the electron’s energy levels inside the QD is the nonlinear Schrödinger equation. With the approximation, the nonlinear Schrödinger equation for a tetrahedral-shaped QD is discretized by using the finite-volume method. The discretized nonlinear Schrödinger equation is solved for the electron energy levels by a computer program. It is noted that the resulting energy levels for the parabolic mass model are nondegenerate due to the mass-gradient term at the corners, edges, and surfaces of the tetrahedral-shaped QD.PACS Nos.: 02.60.Cb, 03.65.Ge, 81.07.Ta

Superstatistics of two electrons quantum dot

2019 ◽  
Vol 34 (03) ◽  
pp. 1950023 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Energy Spectrum ◽  
Thermodynamic Properties ◽  
Quantum Dot ◽  
Schrödinger Equation ◽  
Analytical Method ◽  
Schrodinger Equation ◽  
Boltzmann Factor ◽  
Dirac Delta ◽  
Uniform Distributions ◽  
Parabolic Quantum Dot

In this paper, we discussed the Schrödinger equation in the presence of the harmonic two electrons interaction for the parabolic quantum dot and the energy spectrum by an analytical method is obtained, then the effective Boltzmann factor in a deformed formalism for modified Dirac delta and uniform distributions are derived. We make use of the superstatistics for the two distributions in physics and the thermodynamic properties of the system are calculated. Ordinary results are recovered for the vanishing deformed parameter. Furthermore, the effect of all parameters in the problems are calculated and shown graphically.

EXCITON STATES IN A QUANTUM DOT WITH PARABOLIC CONFINEMENT

2011 ◽  
Vol 25 (32) ◽  
pp. 4489-4497 ◽  
Author(s):  
Ü. DOĞAN ◽  
S. SAKİROĞLU ◽  
A. YILDIZ ◽  
K. AKGÜNGÖR ◽  
H. EPİK ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Quantum Dot ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Center Of Mass ◽  
High Accuracy ◽  
Light Hole ◽  
Parabolic Confinement ◽  
Radial Variable ◽  
Parabolic Quantum Dot

In this study the electronic eigenstructure of an exciton in a parabolic quantum dot (QD) has been calculated with a high accuracy by using Finite element method (FEM). We have converted the coordinates of electron–light-hole system to relative and center of mass coordinate, then placed the Spherical Harmonics into Schrödinger equation analytically and obtained the Schrödinger equation which depends only on the radial variable. Finally we used FEM with only radial variable in order to get the accurate numerical results. We also showed first 21 energy level spectra of exciton depending on confinement and Coulomb interaction parameters.

scholarly journals Quantum dot–ring nanostructure — A comparison of different approaches

2016 ◽  
Vol 30 (13) ◽  
pp. 1642013 ◽  
Author(s):  
Iwona Janus-Zygmunt ◽  
Barbara Kȩdzierska ◽  
Anna Gorczyca-Goraj ◽  
Elżbieta Zipper ◽  
Maciej M. Maśka
Keyword(s):  
Quantum Dot ◽  
Schrödinger Equation ◽  
Transport Properties ◽  
Schrodinger Equation ◽  
Cylindrical Symmetry ◽  
Two Dimensions ◽  
Quantum Ring ◽  
Tight Binding Approximation ◽  
The Third ◽  
Confining Potential

It has been shown recently that a nanostructure composed of a quantum dot (QD) surrounded by a quantum ring (QR) possesses a set of very unique characteristics that make it a good candidate for future nanoelectronic devices. Its main advantage is the ability to easily tune transport properties on demand by so-called “wavefunction engineering”. In practice, the distribution of the electron wavefunction in the nanostructure can be controlled by, e.g., electrical gating. In order to predict some particular properties of the system, one has to know the exact wavefunctions for different shapes of the confining potential that defines the structure. In this paper, we compare three different methods that can be used to determine the energy spectrum, electron wavefunctions and transport properties of the system under investigation. In the first approach, we utilize the cylindrical symmetry of the confining potential and solve only the radial part of the Schrödinger equation; in the second approach, we discretize the Schrödinger equation in two dimensions and find the eigenstates with the help of the Lanczös method; in the third approach, we use package Kwant to solve a tight-binding approximation of the original system. To study the transport properties in all these approaches, we calculate microscopically the strength of the coupling between the nanosystem and leads. In the first two approaches, we use the Bardeen method, in the third one calculations are performed with the help of package Kwant.

Sign in / Sign up

Export Citation Format

Share Document