scholarly journals THREE DIMENSIONAL EXTENSION OF THE EXACT SOLUTI-ONS FOR SCHR?DINGER EQUATION WITH REFLECTIONLESS POTENTIAL

1993 ◽  
Vol 42 (3) ◽  
pp. 345
Author(s):  
ZHOU GUANG-HUI ◽  
WEN GEN-WANG
Keyword(s):  
Three Dimensional ◽  
Dinger Equation ◽  
Reflectionless Potential

EXCITON INSULATOR STATES IN MATERIALS WITH ‘MEXICAN HAT’ BAND STRUCTURE DISPERSION AND IN GRAPHENE

2015 ◽  
Vol 11 (1) ◽  
pp. 2927-2949
Author(s):  
Lyubov E. Lokot
Keyword(s):  
Band Structure ◽  
Three Dimensional ◽  
Dimensional Sphere ◽  
Electron Hole ◽  
Dinger Equation ◽  
Fermi Sphere ◽  
Zinc Blende ◽  
Bulk Gan ◽  
Structure Dispersion ◽  
Excitonic States

In the paper a theoretical study the both the quantized energies of excitonic states and their wave functions in grapheneand in materials with "Mexican hat" band structure dispersion as well as in zinc-blende GaN is presented. An integral twodimensionalSchrödinger equation of the electron-hole pairing for a particles with electron-hole symmetry of reflection isexactly solved. The solutions of Schrödinger equation in momentum space in studied materials by projection the twodimensionalspace of momentum on the three-dimensional sphere are found exactly. We analytically solve an integral twodimensionalSchrödinger equation of the electron-hole pairing for particles with electron-hole symmetry of reflection. Instudied materials the electron-hole pairing leads to the exciton insulator states. Quantized spectral series and lightabsorption rates of the excitonic states which distribute in valence cone are found exactly. If the electron and hole areseparated, their energy is higher than if they are paired. The particle-hole symmetry of Dirac equation of layered materialsallows perfect pairing between electron Fermi sphere and hole Fermi sphere in the valence cone and conduction cone andhence driving the Cooper instability. The solutions of Coulomb problem of electron-hole pair does not depend from a widthof band gap of graphene. It means the absolute compliance with the cyclic geometry of diagrams at justification of theequation of motion for a microscopic dipole of graphene where >1 s r . The absorption spectrums for the zinc-blendeGaN/(Al,Ga)N quantum well as well as for the zinc-blende bulk GaN are presented. Comparison with availableexperimental data shows good agreement.

scholarly journals Direct perturbation method applied to three-dimensional nonlinear Schr?dinger equation

2010 ◽  
Vol 59 (10) ◽  
pp. 6752
Author(s):  
Cheng Xue-Ping ◽  
Lin Ji ◽  
Han Ping
Keyword(s):  
Perturbation Method ◽  
Three Dimensional ◽  
Dinger Equation ◽  
Direct Perturbation

Qualitative analysis of families of bounded solutions of the nonlinear three-dimensional schr�dinger equation

1990 ◽  
Vol 42 (10) ◽  
pp. 1193-1198 ◽  
Author(s):  
I. O. Parasyuk ◽  
V. I. Fushchich
Keyword(s):  
Qualitative Analysis ◽  
Three Dimensional ◽  
Bounded Solutions ◽  
Dinger Equation

Size and Piezoelectric Effects on Optical Properties of Self-Assembled InGaAs/GaAs Quantum Dots

2006 ◽  
Author(s):  
M. K. Kuo ◽  
T. R. Lin ◽  
K. B. Hong
Keyword(s):  
Quantum Dots ◽  
Optical Properties ◽  
Quantum Dot ◽  
Optical Transition ◽  
Energy Levels ◽  
Three Dimensional ◽  
Dinger Equation ◽  
Element Analysis ◽  
Piezoelectric Effects ◽  
Self Assembled

Size effects on optical properties of self-assembled quantum dots are analyzed based on the theories of linear elasticity and of strain-dependent k-p with the aid of finite element analysis. The quantum dot is made of InGaAs with truncated pyramidal shape on GaAs substrate. The three-dimensional steady-state effective-mass Schro¨dinger equation is adopted to find confined energy levels as well as wave functions both for electrons and holes of the quantum-dot nanostructures. Strain-induced as well as piezoelectric effects are taken into account in the carrier confinement potential of Schro¨dinger equation. The optical transition energies of quantum dots, computed from confined energy levels for electrons and holes, are significantly different for several quantum dots with distinct sizes. It is found that for QDs with the the larger the volume of QD is, the smaller the values of the optical transition energy. Piezoelectric effect, on the other hand, splits the p-like degeneracy for the electron first excited state about 1~7 meV, and leads to anisotropy on the wave function.

scholarly journals EXACT SOLUTION OF SCHR?DINGER EQUATION WITH REFLECTIONLESS POTENTIAL WELL

1993 ◽  
Vol 42 (2) ◽  
pp. 173
Author(s):  
ZHOU GUANG-HUI
Keyword(s):  
Exact Solution ◽  
Potential Well ◽  
Dinger Equation ◽  
Reflectionless Potential

scholarly journals Analytical solutions of the three-dimensional Schr?dinger equation with an exponentially changing effective mass

2005 ◽  
Vol 54 (6) ◽  
pp. 2528
Author(s):  
Cai Chang-Ying ◽  
Ren Zhong-Zhou ◽  
Ju Guo-Xing
Keyword(s):  
Effective Mass ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Dinger Equation

scholarly journals Numerical solution of the three-dimensional time-dependent Schr?dinger equation and its application

2009 ◽  
Vol 58 (12) ◽  
pp. 8180
Author(s):  
Zeng Si-Liang ◽  
Zou Shi-Yang ◽  
Wang Jian-Guo ◽  
Yan Jun
Keyword(s):  
Numerical Solution ◽  
Three Dimensional ◽  
Time Dependent ◽  
Dinger Equation

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Sign in / Sign up

Export Citation Format

Share Document