A novel numerical technique for solving the one-dimensional Schroedinger equation using matrix approach-application to quantum well structures

1988 ◽  
Vol 24 (8) ◽  
pp. 1524-1531 ◽  
Author(s):  
A.K. Ghatak ◽  
K. Thyagarajan ◽  
M.R. Shenoy
Keyword(s):  
Quantum Well ◽  
Numerical Technique ◽  
Schroedinger Equation ◽  
Matrix Approach ◽  
Quantum Well Structures ◽  
One Dimensional ◽  
The One

scholarly journals Photon confinement in one-dimensional photonic quantum-well structures of nanoporous silicon

2003 ◽  
Vol 126 (3) ◽  
pp. 125-128 ◽  
Author(s):  
S.H. Xu ◽  
Z.H. Xiong ◽  
L.L. Gu ◽  
Y. Liu ◽  
X.M. Ding ◽  
...  
Keyword(s):  
Quantum Well ◽  
Nanoporous Silicon ◽  
Quantum Well Structures ◽  
One Dimensional ◽  
Photon Confinement ◽  
Photonic Quantum Well

Effect of the Spatial Extent of the Control in a Bilinear Control Problem for the Schroedinger Equation

2009 ◽  
Author(s):  
Katherine A. Kime
Keyword(s):  
Differential Geometry ◽  
Finite Difference ◽  
Lie Algebras ◽  
Grid Point ◽  
Schroedinger Equation ◽  
Time Varying ◽  
One Dimensional ◽  
Bilinear Control ◽  
The One ◽  
Bilinear Control Problem

We consider control of the one-dimensional Schroedinger equation through a time-varying potential. Using a finite difference semi-discretization, we consider increasing the extent of the potential from a single central grid-point in space to two or more gridpoints. With the differential geometry package in Maple 8, we compute and compare the corresponding Control Lie Algebras, identifying a trend in the number of elements which span the Control Lie Algebras.

Particle-hole pair and beelectron states in ZnO/(Zn,Mg)O quantum wells and Dirac materials.

2015 ◽  
Vol 10 (1) ◽  
pp. 2583-2604
Author(s):  
Lyubov E. Lokot
Keyword(s):  
Quantum Well ◽  
Charge Density ◽  
Heavy Hole ◽  
Wave Functions ◽  
One Dimensional ◽  
Exchange Correlation ◽  
Hartree Fock ◽  
Exchange Correlation Potential ◽  
Correlation Potential ◽  
The One

In this paper a theoretical studies of the space separation of electron and hole wave functions in the quantum well ZnO/Mg(0.27)Zn(0.73)O are presented. For this aim the self-consistent solution of the Schrödinger equations for electrons and holes and the Poisson equations at the presence of spatially varying quantum well potential due to the piezoelectric effect and local exchange-correlation potential is found. The one-dimensional Poisson equation contains the Hartree potential which includes the one-dimensional charge density for electrons and holes along the polarization field distribution. The three-dimensional Poisson equation contains besides the one-dimensional charge density for electrons and holes the exchange-correlation potential which is built on convolutions of a plane-wave part of wave functions in addition. The shifts of the Hartree valence band spectrums and the conduction band spectrum with respect to the flat band spectrums as well as the Hartree-Fock band spectrums with respect to the Hartree ones are found. An overlap integrals of the wave functions of holes and electron with taking into account besides the piezoelectric effects the exchange-correlation effects in addition is greater than an overlap integral of Hartree ones. The Hartree particles distribute greater on edges of quantum well than Hartree-Fock particles. It is found that an effective mass of heavy hole of Mg(0.27)Zn(0.73)O under biaxial strain is greater than an effective-mass of heavy hole of ZnO. It is calculated that an electron mass is less than a hole mass. It is found that the Bohr radius is grater than the localization range particle-hole pair, and the excitons may be spontaneously created.Schrödinger equation for pair of two massless Dirac particles when magnetic field is applied in Landau gauge is solved exactly. In this case the separation of center of mass and relative motion is obtained. Landau quantization $\epsilon=\pm\,B\sqrt{l}$ for pair of two Majorana fermions coupled via a Coulomb potential from massless chiral Dirac equation in cylindric coordinate is found. The root ambiguity in energy spectrum leads into Landau quantization for beelectron, when the states in which the one simultaneously exists are allowed. The tachyon solution with imaginary energy in Cooper problem ($\epsilon^{2}<0$) is found.

One-dimensional photonic crystals based on periodic multiple quantum well structures

2005 ◽  
Vol 2 (2) ◽  
pp. 805-808 ◽  
Author(s):  
L. I. Deych ◽  
M. V. Erementchouk ◽  
E. L. Ivchenko ◽  
A. A. Lisyansky ◽  
M. M. Voronov
Keyword(s):  
Photonic Crystals ◽  
Quantum Well ◽  
Multiple Quantum Well ◽  
Multiple Quantum ◽  
Quantum Well Structures ◽  
One Dimensional
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