Méthode du moment angulaire inversé. Partie I : La théorie MI

1975 ◽  
Vol 53 (5) ◽  
pp. 533-541 ◽  
Author(s):  
J-L. Féménias ◽  
C. Athénour
Keyword(s):  
Angular Momentum ◽  
Wave Functions ◽  
Matrix Elements ◽  
Intensity Factors ◽  
Normal Theory ◽  
Commutation Relations ◽  
Minus Sign ◽  
Mi Theory ◽  
Optimal Set ◽  
General Method

In order to present a general method of calculating wave functions, matrix elements, and intensity factors in molecular rotational problems, we deal here with a theory of reversed angular momentum (MI theory), i.e. momentum whose components obey commutation relations with an anomalous minus sign. This theory is built following the principal corresponding steps of the normal theory and a simple correspondence is established between both of them allowing us to perform calculations in the former and to give the results using the formalism of the latter.In particular we dwell here on the consistency of conventions and notations and on a rigorous presentation of spherical tensor operators in MI theory together with the choice of the optimal set of them leading to simplest calculations.

Méthode du moment angulaire inversé. Partie II : Application aux problèmes hyperfins diatomiques

1975 ◽  
Vol 53 (5) ◽  
pp. 542-552 ◽  
Author(s):  
J-L. Féménias ◽  
C. Athénour
Keyword(s):  
Angular Momentum ◽  
Experimental Verification ◽  
Experimental Results ◽  
Matrix Elements ◽  
Intensity Factors ◽  
Method Of Calculation ◽  
Straightforward Method ◽  
Mi Theory

We present a straightforward method of calculation in rotational molecular problems based on the theory of reversed angular momentum (MI theory) previously discussed. After some general remarks and calculations, we test this method by calculating some well known hyperfine matrix elements in diatomic problems, showing thus its easy handling. The first experimental verification relative to intensity factors in hyperfine diatomic transitions that the method enabled us to calculate, is presented with a brief survey of the recent experimental results obtained from the analysis of the [Formula: see text] system of NbN.

Etude des molécules diatomiques. Partie II : Intensités

1977 ◽  
Vol 55 (20) ◽  
pp. 1775-1786
Author(s):  
Jean-Louis Féménias
Keyword(s):  
Emission Spectrum ◽  
Electronic States ◽  
Optical Emission ◽  
Wave Functions ◽  
Effective Hamiltonian ◽  
Intensity Factors ◽  
Optical Emission Spectrum ◽  
Analytical Expressions ◽  
General Method ◽  
Numerical Approaches

Theory of perturbations, giving the diatomic effective Hamiltonian, is used for calculating actual molecular wave functions and intensity factors involved in transitions between states arising from Hund's coupling cases a, b, intermediate a–b, and c tendency. The Herman and Wallis corrections are derived, without any knowledge of the analytical expressions of the wave functions, and generalized to transitions between electronic states with whatever symmetry and multiplicity. A general method for studying perturbed intensities is presented, taking in good part the spectroscopic modern numerical approaches. The method is used in the study of the ScO optical emission spectrum.

scholarly journals DIRAC OPERATORS ON QUANTUM-TWO SPHERES

1994 ◽  
Vol 09 (25) ◽  
pp. 2325-2333 ◽  
Author(s):  
KAZUTOSHI OHTA ◽  
HISAO SUZUKI
Keyword(s):  
Angular Momentum ◽  
Dirac Operator ◽  
Quantum Group ◽  
Total Angular Momentum ◽  
Dirac Operators ◽  
Wave Functions ◽  
Commutation Relations ◽  
Pauli Matrices

We investigate the spin-1/2 fermions on quantum-two spheres. It is shown that the wave functions of fermions and a Dirac operator on quantum-two spheres can be constructed in a manifestly covariant way under the quantum group SU (2)q. The concept of total angular momentum and chirality can be expressed by using q-analog of Pauli-matrices and appropriate commutation relations.

THE HIDDEN SYMMETRY FOR A QUANTUM SYSTEM WITH A PÖSCHL–TELLER-LIKE POTENTIAL

2003 ◽  
Vol 12 (06) ◽  
pp. 809-815 ◽  
Author(s):  
SHI-HAI DONG ◽  
GUO-HUA SUN ◽  
YU TANG
Keyword(s):  
Quantum System ◽  
Wave Functions ◽  
Matrix Elements ◽  
Eigenvalues And Eigenfunctions ◽  
Creation And Annihilation Operators ◽  
Commutation Relations ◽  
Hidden Symmetry ◽  
The Matrix ◽  
The Creation ◽  
Analytical Expressions

The eigenvalues and eigenfunctions of the Schrödinger equation with a Pöschl–Teller (PT)-like potential are presented. A realization of the creation and annihilation operators for the wave functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions, sin (ρ) and [Formula: see text] with ρ=πx/L.

Tensorial calculations in molecular spectroscopy

1979 ◽  
Vol 57 (11) ◽  
pp. 2030-2044
Author(s):  
Jean-Louis Féménias
Keyword(s):  
Angular Momentum ◽  
Molecular Spectroscopy ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Intensity Factors ◽  
Molecular Physics ◽  
Mechanical Formulation ◽  
The Matrix ◽  
Tensor Operators

A strict quantum mechanical formulation of Van Vleck's concept of Reversed Angular Momentum is given. This generalization leads to a method suitable for the calculation of the matrix elements of all kinds of tensor operators in molecular physics. Applications and examples are described for the diatomic case. Various interactions—in the non-rotating or in the rotating molecule—are studied, and some intensity factors are derived in an original way. In all cases, the simplicity, generality, rapidity, and consistency of the method are tested and, where relevant, compared with other techniques.

AN ALGEBRAIC APPROACH TO A HARMONIC OSCILLATOR PLUS AN INVERSE SQUARE POTENTIAL IN TWO DIMENSIONS

2005 ◽  
Vol 20 (24) ◽  
pp. 5663-5670 ◽  
Author(s):  
SHI-HAI DONG ◽  
GUO-HUA SUN ◽  
M. LOZADA-CASSOU
Keyword(s):  
Harmonic Oscillator ◽  
Exact Solutions ◽  
Algebraic Approach ◽  
Two Dimensions ◽  
Wave Functions ◽  
Matrix Elements ◽  
Ladder Operators ◽  
Radial Wave ◽  
Commutation Relations ◽  
The Matrix

The exact solutions of the Schrödinger equation with a harmonic oscillator plus an inverse square potential are obtained in two dimensions. We construct the ladder operators directly from the radial wave functions and find that these operators satisfy the commutation relations of an SU (1, 1) group. We obtain the explicit expressions of the matrix elements for some related functions ρ and [Formula: see text] with ρ = r2. We also explore another symmetry between the eigenvalues E(r) and E(ir) by substituting r→ir.

Low-lying collective bands in the even tungsten isotopes 180–186W

1989 ◽  
Vol 67 (5) ◽  
pp. 479-484 ◽  
Author(s):  
R. Sahu
Keyword(s):  
Wave Function ◽  
Angular Momentum ◽  
Quadrupole Interaction ◽  
Asymmetry Parameter ◽  
Degrees Of Freedom ◽  
Energy Levels ◽  
Wave Functions ◽  
Electromagnetic Properties ◽  
Matrix Elements ◽  
Rigid Model

The γ-rigid model has been used to study the energy levels and the electromagnetic properties of 180, 182, 184, 186W. In this model, the intrinsic wave functions are obtained using the pairing plus the quadrupole–quadrupole interaction Hamiltonian of Baranger and Kumar. Good angular momentum states are projected approximately from such a triaxially symmetric intrinsic wave function. This model assumes the nucleus to be γ rigid but soft in the β degrees of freedom. The asymmetry parameter γ for a given nucleus is extracted using the experimental energies of the first 2+ and second 2+ states within the framework of the Davydov–Filippov model. The symmetry parameter β for each J state is determined from the minimization of the projected energy. The calculated energy levels of the ground and the 7 band, the B(E2) values, the electromagnetic moments, the E2 and E4 matrix elements, and the B(E2) ratios agree quite well with experimental results.

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