scholarly journals Unique continuation for the Schrödinger equation with gradient term

2018 ◽  
Vol 146 (6) ◽  
pp. 2555-2562
Author(s):  
Youngwoo Koh ◽  
Ihyeok Seo
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Unique Continuation ◽  
Gradient Term

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 Unique continuation for the magnetic Schrödinger equation

2020 ◽  
Vol 120 (8) ◽  
Author(s):  
Andre Laestadius ◽  
Michael Benedicks ◽  
Markus Penz
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Unique Continuation

On a unique continuation for Aharonov–Bohm magnetic Schrödinger equation

2017 ◽  
Vol 29 (6) ◽  
Author(s):  
Mohammed El Aïdi
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Unique Continuation ◽  
Compact Set ◽  
Two Dimensional ◽  
Aharonov Bohm

AbstractWe furnish a unique continuation for a suitable two-dimensional magnetic Schrödinger equation defined on the complement of a compact set.

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