Coulomb interaction in the one-dimensional free-electron model

1969 ◽  
Vol 14 (3) ◽  
pp. 184-191
Author(s):  
P. John Roberts
Keyword(s):  
Coulomb Interaction ◽  
Free Electron ◽  
Electron Model ◽  
One Dimensional ◽  
Free Electron Model ◽  
The One

Self-organizing atom chains

2017 ◽  
Author(s):  
Arie van Houselt ◽  
Harold J.W. Zandvliet
Keyword(s):  
Free Electron ◽  
Electrostatic Interactions ◽  
Dimensional System ◽  
Electron Systems ◽  
Electron Model ◽  
One Dimensional ◽  
Free Electron Model ◽  
Peierls Instability ◽  
The One ◽  
Self Organizing

This article examines the intriguing physical properties of nanowires, with particular emphasis on self-organizing atom chains. It begins with an overview of the one-dimensional free electron model and some interesting phenomena of one-dimensional electron systems. It derives an expression for the 1D density of states, which exhibits a singularity at the bottom of the band and extends the free-electron model, taking into consideration a weak periodic potential that is induced by the lattice. It also describes the electrostatic interactions between the electrons and goes on to discuss two interesting features of 1D systems: the quantization of conductance and Peierls instability. Finally, the article presents the experimental results of a nearly ideal one-dimensional system, namely self-organizing platinum atom chains on a Ge(001) surface, focusing on their formation, quantum confinement between the Pt chains and the occurrence of a Peierls transition within the chains.

The light absorption of vitamin B 12

1965 ◽  
Vol 288 (1414) ◽  
pp. 348-351 ◽  
Keyword(s):  
Light Absorption ◽  
Standard Procedure ◽  
Vitamin B ◽  
Electron Model ◽  
One Dimensional ◽  
Axial Ligands ◽  
Free Electron Model ◽  
Vitamin B 12 ◽  
Three Stages ◽  
The One

A calculation based on the one dimensional free electron model of the light absorption of vitamin B 12 and of similar compounds has been carried out. The model was applied in its simplest form and in three stages of refinement by using a standard procedure described in a recent paper (Kuhn 1964) and tested there on a great number of dyes. The calculation was thus straightforward and no adjustable parameters were introduced. The interaction of the chromophore with the axial ligands was neglected as well as any effect depending on the specific nature of the central atom or on the buckling of the resonating portion.

STATISTICS ON NETWORKS

1992 ◽  
Vol 07 (19) ◽  
pp. 4633-4654 ◽  
Author(s):  
A.P. BALACHANDRAN ◽  
E. ERCOLESSI
Keyword(s):  
Single Particle ◽  
Free Electron ◽  
Quantum Physics ◽  
Two Dimensions ◽  
Topological Spaces ◽  
Electron Model ◽  
One Dimensional ◽  
Free Electron Model ◽  
Points Of View ◽  
Particle Statistics

One-dimensional networks are excellent examples of topological spaces which are not manifolds and which admit interesting quantum physics. They are of importance in the free electron model for molecules and crystals. They also occur as fabricated mesoscopic networks. We review single-particle quantum physics on networks from topological and operator theoretic points of view and then initiate study of identical particles on networks. It is established that the available statistics on networks in its range and complexity rival the richness of statistical options in two dimensions. We treat two-particle statistics on simple networks with detail, taking care to cover operator theoretic issues pertaining to multiple connectivity and also those due to basic topological differences between a generic network and a manifold.

SFA applied to the one-dimensional two-electron model atom

1995 ◽  
Vol 28 (20) ◽  
pp. 4413-4419 ◽  
Author(s):  
J Bauer ◽  
M Ivanov ◽  
K Rzazewski ◽  
H R Reiss
Keyword(s):  
Electron Model ◽  
One Dimensional ◽  
The One ◽  
Model Atom

scholarly journals FREE ELECTRON MODEL STUDY ON INTERLAYER EXCHANGE COUPLING IN MAGNETIC MULTILAYERS

1996 ◽  
Vol 45 (5) ◽  
pp. 869
Author(s):  
YANG GUO-LIN ◽  
LI BO-ZANG ◽  
LI LIE-MING ◽  
SUN GANG ◽  
WU JIAN-HUA ◽  
...  
Keyword(s):  
Free Electron ◽  
Exchange Coupling ◽  
Magnetic Multilayers ◽  
Interlayer Exchange Coupling ◽  
Electron Model ◽  
Model Study ◽  
Free Electron Model ◽  
Interlayer Exchange
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