Selection Rules and Matrix Elements

1996 ◽  
pp. 183-202
Author(s):  
Wolfgang Ludwig ◽  
Claus Falter
Keyword(s):  
Matrix Elements ◽  
Selection Rules

SYMMETRY AND ELECTRO-OPTICAL PROPERTIES OF NANOTUBES

2002 ◽  
Vol 01 (03n04) ◽  
pp. 313-325 ◽  
Author(s):  
M. DAMNJANOVIĆ ◽  
I. MILOŠEVIĆ ◽  
T. VUKOVIĆ ◽  
B. NIKOLIĆ ◽  
E. DOBARDŽIĆ
Keyword(s):  
Carbon Nanotubes ◽  
Optical Properties ◽  
Density Functional ◽  
Tight Binding ◽  
Optical Characteristics ◽  
Optical Transitions ◽  
Matrix Elements ◽  
Selection Rules ◽  
Single Wall Carbon ◽  
Quantum Numbers

The symmetry of single-wall carbon and inorganic tubes is reviewed. For the carbon nanotubes it is used to get the full set of quantum numbers, in the efficient precision (combined density functional and tight-binding methods) calculation of electronic bands and their complete assignation, to obtain the selection rules for optical transitions and the momenta matrix elements for the Bloch eigen-states. The optical characteristics are thoroughly found, and discussed.

scholarly journals Intersubband resonances in InAs/AlSb quantum wells: Selection rules, matrix elements, and the depolarization field

1996 ◽  
Vol 53 (12) ◽  
pp. 7903-7910 ◽  
Author(s):  
R. J. Warburton ◽  
C. Gauer ◽  
A. Wixforth ◽  
J. P. Kotthaus ◽  
B. Brar ◽  
...  
Keyword(s):  
Quantum Wells ◽  
Matrix Elements ◽  
Selection Rules

scholarly journals Explicit expressions for totally symmetric spherical functions and symmetry-dependent properties of multipoles

2014 ◽  
Vol 470 (2171) ◽  
pp. 20140435
Author(s):  
Boris Zapol ◽  
Peter Zapol
Keyword(s):  
Point Group ◽  
Product Structure ◽  
Spherical Functions ◽  
Matrix Elements ◽  
Linear Combinations ◽  
Selection Rules ◽  
Charge Distributions ◽  
Symmetry Operators ◽  
Point Groups ◽  
Symmetry Operations

Closed expressions for matrix elements 〈 lm' | A (G)| lm 〉, where | lm 〉 are spherical functions and A (G) is the average of all symmetry operators of point group G, are derived for all point groups (PGs) and then used to obtain linear combinations of spherical functions that are totally symmetric under all symmetry operations of G. In the derivation, we exploit the product structure of the groups. The obtained expressions are used to explore properties of multipoles of symmetric charge distributions. We produce complete lists of selection rules for multipoles Q l and their moments Q lm , as well as of numbers of independent moments in a multipole, for any l and m and for all PGs. Periodicities and other trends in these properties are revealed.

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