Analytical Evaluation of Two-Center Franck-Condon Overlap Integrals over Harmonic Oscillator Wave Function

2006 ◽  
Vol 61 (3-4) ◽  
pp. 141-145 ◽  
Author(s):  
Israfil I. Guseinov ◽  
Bahtiyar A. Mamedov ◽  
Arife S. Ekenoğlu
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Numerical Results ◽  
Binomial Coefficients ◽  
Overlap Integrals ◽  
Analytical Evaluation ◽  
Cpu Time ◽  
Oscillator Wave Function ◽  
Harmonic Oscillator Wave Function ◽  
Franck Condon

A unified treatment of Franck-Condon (FC) overlap integrals with arbitrary values of parameters is described. These integrals are represented in terms of binomial coefficients. For quick calculations, the binomial coefficients are stored in the memory of the computer. Therefore, the CPU time has been greatly reduced. Numerical results presented agree excellently with those obtained in the literature

scholarly journals COLOR-STRAIGHT FOUR-QUARK OPERATORS AND LIFETIMES OF b-FLAVORED HADRONS

2000 ◽  
Vol 15 (19) ◽  
pp. 3053-3063
Author(s):  
S. ARUNAGIRI
Keyword(s):  
Wave Function ◽  
Form Factor ◽  
Harmonic Oscillator ◽  
Oscillator Strength ◽  
Light Quark ◽  
Numerical Prediction ◽  
Expectation Values ◽  
Oscillator Wave Function ◽  
Harmonic Oscillator Wave Function ◽  
Quark Scattering

Using the relation between the harmonic oscillator wave function and the light quark scattering form factor, the expectation values of color-straight four-quark operators are evaluated and found to be directly proportional to the cubic power of the oscillator strength. It is predicted that the ratio τ(Λb)/τ(B)≈0.79(0.84) due to the factorizable (nonfactorizable) piece, against the experimental 0.79±0.06. Notwithstanding the numerical prediction, the present study shows that the four-quark operators play a role as far the lifetimes of b-flavored hadrons are concerned.

CHARMONIUM SPECTRA AND DECAYS IN A SEMIRELATIVISTIC MODEL

2012 ◽  
Vol 27 (22) ◽  
pp. 1250127 ◽  
Author(s):  
BHAGHYESH ◽  
K. B. VIJAYA KUMAR
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Mass Spectra ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Model Parameters ◽  
Decay Properties ◽  
Oscillator Wave Function ◽  
Harmonic Oscillator Wave Function ◽  
Relativistic Kinetic Energy

We investigate the spectra and decays of charmonium [Formula: see text] system in a semirelativistic potential model. The Hamiltonian of our model consists of a relativistic kinetic energy term, a vector Coulomb-like potential and a scalar confining potential. From this Hamiltonian a spinless wave equation is obtained. The wave equation is then reduced to the form of a single particle Schrödinger equation. The spin dependent potentials are introduced as a perturbation. The three-dimensional harmonic oscillator wave function is employed as a trial wave function and the [Formula: see text] mass spectra is obtained by the variational method. The model parameters and the wave function that reproduce the mass spectra of the [Formula: see text] mesons are then used to investigate some of the decay properties. The results obtained are then compared with the experimental data and with the predictions of other theoretical models. We also propose possible [Formula: see text] assignments for the recently observed charmonium or charmonium-like states.

On a Unified Theory of Twocentre Harmonic Oscillator Integrals

1971 ◽  
Vol 26 (6) ◽  
pp. 943-946 ◽  
Author(s):  
W . Wltschel
Keyword(s):  
Kinetic Energy ◽  
Harmonic Oscillator ◽  
Operator Technique ◽  
Unified Theory ◽  
Overlap Integrals ◽  
Second Quantization ◽  
Energy Integrals ◽  
Franck Condon

Abstract Twocentre harmonic oscillator overlap integrals (Franck-Condon-integrals) are calculated in a simple way for twodimensional oscillators of different frequencies. Second quantization and operator technique are applied. It is further shown that transition and kinetic energy integrals can be derived in the same representation.

scholarly journals On a Unified Theory of Twocentre Harmonic Oscillator Integrals I. The Onedimensional Oscillator

1971 ◽  
Vol 26 (6) ◽  
pp. 940-942
Author(s):  
W . Wltschel
Keyword(s):  
Harmonic Oscillator ◽  
Collision Energy ◽  
Unified Theory ◽  
Overlap Integrals ◽  
Second Quantization ◽  
Quantization Representation ◽  
Franck Condon

Abstract Twocentre harmonic oscillator overlap integrals, arbitrary transition integrals and collision energy etchange integrals for equal and different frequencies of the oscillators are contained in a generalized Franck-Condon-integral which is solved by operator methods in the second quantization representation.

USE OF BINOMIAL COEFFICIENTS IN FAST AND ACCURATE CALCULATION OF CLEBSCH–GORDAN AND GAUNT COEFFICIENTS, AND WIGNER n - j SYMBOLS

2009 ◽  
Vol 08 (02) ◽  
pp. 251-259 ◽  
Author(s):  
I. I. GUSEINOV ◽  
B. A. MAMEDOV ◽  
E. ÇOPUROĞLU
Keyword(s):  
Efficient Algorithms ◽  
Numerical Results ◽  
Binomial Coefficients ◽  
Evaluation Procedure ◽  
Complete Agreement ◽  
Accurate Calculation ◽  
Fast Calculation ◽  
Alternative Evaluation ◽  
Cpu Time

Using binomial coefficients, the new simple and efficient algorithms for the accurate and fast calculation of the Clebsch–Gordan and Gaunt coefficients, and Wigner n - j symbols for n = 3, 6, 9 are presented. For quick calculations, the binomial coefficients are stored in the memory of the computer. It is demonstrated that the use of binomial coefficients greatly reduces the CPU time. The numerical results presented are in complete agreement with those obtained in the alternative evaluation procedure. The method suggested is completely general and free of any restrictions.

WEAK LEPTONIC DECAY OF LIGHT AND HEAVY PSEUDOSCALAR MESONS IN A FIELD-THEORETIC QUARK MODEL

1993 ◽  
Vol 08 (29) ◽  
pp. 2775-2783 ◽  
Author(s):  
L. MAHARANA ◽  
A. NATH ◽  
A. R. PANDA
Keyword(s):  
Harmonic Oscillator ◽  
Quark Model ◽  
Constituent Quark ◽  
Leptonic Decay ◽  
Decay Constants ◽  
Quark Masses ◽  
Leptonic Decays ◽  
Pseudoscalar Mesons ◽  
Oscillator Wave Function ◽  
Harmonic Oscillator Wave Function

Weak leptonic decays of light and heavy pseudoscalar mesons are studied in a field-theoretic quark model where the mesons are described by constituent quarks and antiquarks with a particular ansatz and a Harmonic oscillator wave function. With constituent quark masses and Harmonic oscillator radii for mesons as parameters of the model, decay constants are calculated and found as (fπ, fk, fD, fB) = (132 MeV , 161 MeV , 160 MeV , 115 MeV ) indicating a reasonable agreement with the experimental data wherever available. Partial decay widths and branching ratios for kinematically allowed leptonic decay processes are also estimated and compared with the experiments wherever available.

scholarly journals Energy and Wave function Analysis on Harmonic Oscillator Under Simultaneous Non-Hermitian Transformations of Co-ordinate and Momentum: Iso-spectral case

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 492-497
Author(s):  
Biswanath Rath ◽  
P. Mallick
Keyword(s):  
Wave Function ◽  
Perturbation Theory ◽  
Harmonic Oscillator ◽  
Function Analysis ◽  
Energy Eigenvalue ◽  
Algebraic Approach ◽  
Wave Function Analysis ◽  
Wavefunction Analysis

AbstractWe present a complete energy and wavefunction analysis of a Harmonic oscillator with simultaneous non-hermitian transformations of co-ordinate $(x \rightarrow \frac{(x + i\lambda p)}{\sqrt{(1+\beta \lambda)}})$ and momentum $(p \rightarrow \frac {(p+i\beta x)}{\sqrt{(1+\beta \lambda)}})$ using perturbation theory under iso-spectral conditions. We observe that two different frequencies of oscillation (w1, w2)correspond to the same energy eigenvalue, - which can also be verified using a Lie algebraic approach.

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