Even-wave harmonic-oscillator theory of baryonic states. II. Orbital matrix elements and selection rules

1977 ◽  
Vol 15 (7) ◽  
pp. 1991-1996 ◽  
Author(s):  
A. N. Mitra ◽  
Sudhir Sood
Keyword(s):  
Harmonic Oscillator ◽  
Matrix Elements ◽  
Selection Rules ◽  
Oscillator Theory

Matrix elements of the radial-angular factorized harmonic oscillator

1972 ◽  
Vol 12 (2) ◽  
pp. 185-196 ◽  
Author(s):  
T. G. Haskell ◽  
B. G. Wyboturne
Keyword(s):  
Harmonic Oscillator ◽  
Matrix Elements

Matrix Elements of the Lorentzian Term

1976 ◽  
Vol 31 (6) ◽  
pp. 553-556 ◽  
Author(s):  
Ch. V. S. Ramachandrá Rao
Keyword(s):  
Harmonic Oscillator ◽  
Matrix Elements ◽  
Practical Application ◽  
The Matrix

Recursion formulae for the matrix elements of the Lorentzian term 1/(C2 + q2) as well as 1/(C2 + q2)2, on the basis of harmonic oscillator eigenfunctions, are obtained. A practical application where these formulae would be useful is discussed

Quantum algebras and parity-dependent spectra

2007 ◽  
Vol 463 (2086) ◽  
pp. 2415-2427 ◽  
Author(s):  
C.V Sukumar ◽  
Andrew Hodges
Keyword(s):  
Quantum Optics ◽  
Harmonic Oscillator ◽  
Combinatorial Theory ◽  
Squeezed States ◽  
Quantum Algebras ◽  
Matrix Elements ◽  
Euler Numbers ◽  
Simple Harmonic Oscillator ◽  
Non Gaussian ◽  
Special Case

We study the structure of a quantum algebra in which a parity-violating term modifies the standard commutation relation between the creation and annihilation operators of the simple harmonic oscillator. We discuss several useful applications of the modified algebra. We show that the Bernoulli and Euler numbers arise naturally in a special case. We also show a connection with Gaussian and non-Gaussian squeezed states of the simple harmonic oscillator. Such states have been considered in quantum optics. The combinatorial theory of Bernoulli and Euler numbers is developed and used to calculate matrix elements for squeezed states.

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.

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