scholarly journals Virtual-bound, filamentary and layered states in a box-shaped quantum dot of square potential form the exact numerical solution of the effective mass Schrödinger equation

2013 ◽  
Vol 413 ◽  
pp. 73-81 ◽  
Author(s):  
A. Luque ◽  
A. Mellor ◽  
I. Tobías ◽  
E. Antolín ◽  
P.G. Linares ◽  
...  
Keyword(s):  
Quantum Dot ◽  
Schrödinger Equation ◽  
Numerical Solution ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Exact Numerical Solution ◽  
Effective Mass Schrödinger Equation ◽  
Potential Form

Exactly solvable effective mass Schrödinger equation with coulomb-like potential

2010 ◽  
Vol 110 (15) ◽  
pp. 2880-2885 ◽  
Author(s):  
C. Pacheco-García ◽  
J. García-Ravelo ◽  
J. Morales ◽  
J. J. Peña
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Effective Mass Schrödinger Equation ◽  
Exactly Solvable

A solution of the effective-mass Schrödinger equation in general isotropic and nonparabolic bands for the study of two-dimensional carrier gases

2005 ◽  
Vol 98 (3) ◽  
pp. 033717 ◽  
Author(s):  
F. M. Gómez-Campos ◽  
S. Rodríguez-Bolívar ◽  
J. A. López-Villanueva ◽  
J. A. Jiménez-Tejada ◽  
J. E. Carceller
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Two Dimensional ◽  
Effective Mass Schrödinger Equation ◽  
Carrier Gases

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

scholarly journals A GENERAL SCHEME FOR THE EFFECTIVE-MASS SCHRÖDINGER EQUATION AND THE GENERATION OF THE ASSOCIATED POTENTIALS

2004 ◽  
Vol 19 (37) ◽  
pp. 2765-2775 ◽  
Author(s):  
B. BAGCHI ◽  
P. GORAIN ◽  
C. QUESNE ◽  
R. ROYCHOUDHURY
Keyword(s):  
Schrödinger Equation ◽  
Effective Mass ◽  
Schrodinger Equation ◽  
Bound States ◽  
General Scheme ◽  
Free Particle ◽  
Energy Operator ◽  
Unified Approach ◽  
One Dimensional ◽  
Effective Mass Schrödinger Equation

A systematic procedure to study one-dimensional Schrödinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting situation in that, in the presence of a mass background, formation of bound states is signalled. We also discuss coordinate-transformed, constant-mass Schrödinger equation, its matching with the PDEM form and the consequent decoupling of the ambiguity parameters. This provides a unified approach to many exact results known in the literature, as well as to a lot of new ones.

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