scholarly journals Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries

Symmetry ◽  
2012 ◽  
Vol 4 (4) ◽  
pp. 667-685 ◽  
Author(s):  
Renato Lemus
Keyword(s):  
Discrete Symmetries ◽  
Quantum Numbers ◽  
Symmetry Adapted Functions

Algebraic expressions for symmetry-adapted functions of the icosahedral group in spinor space

1999 ◽  
Vol 55 (6) ◽  
pp. 1049-1060 ◽  
Author(s):  
Peng-Dong Fan ◽  
Jin-Quan Chen ◽  
J. P. Draayer
Keyword(s):  
Angular Momentum ◽  
Projection Operators ◽  
Icosahedral Group ◽  
Quantum Numbers ◽  
Algebraic Expressions ◽  
Group I ◽  
Spinor Space ◽  
Symmetry Adapted Functions ◽  
Eigenfunction Method

Algebraic expressions for projection operators and symmetry-adapted functions (SAFs) of the icosahedral group for spinor (double-valued) representations are found by using the double-induced technique and eigenfunction method. The SAFs are functions of the angular momentum j, the quantum numbers \lambda, \nu, \mu of the group chain I \supset D_5 \supset C_5, and the multiplicity label \bar m. By this procedure, SAFs for the group I are provided once for all instead of one j value at a time.

Reduced projection operators and algebraic expressions for the symmetry-adapted functions of the icosahedral group

1999 ◽  
Vol 55 (5) ◽  
pp. 871-883 ◽  
Author(s):  
Peng-Dong Fan ◽  
Jin-Quan Chen ◽  
J. P. Draayer
Keyword(s):  
Angular Momentum ◽  
Cyclic Subgroup ◽  
Double Coset ◽  
Projection Operators ◽  
Icosahedral Group ◽  
Quantum Numbers ◽  
Algebraic Expressions ◽  
Group I ◽  
Symmetry Adapted Functions ◽  
Eigenfunction Method

The algebraic expressions for the reduced projection operators \wp^{(\lambda)\bar{\mu}}_{\mu} = \sum_{i = 1}^4 u_i \hat{\beta_i} for the irreducible representation (irrep) \lambda of the icosahedral group I are found by using the double-induced technique and eigenfunction method, where \hat{\beta}_i are the double-coset generators of I with respect to the cyclic subgroup C_5. Simple algebraic expressions are derived for the symmetry-adapted functions (SAF's) by applying the reduced projection operators \wp^{(\lambda) \bar{\mu}}_\mu to Y_{l \bar m}. The SAF's are functions of the angular momentum l, the quantum numbers \lambda, \mu of the group chain I \supset C_5 and the multiplicity label \bar m. In this way, the SAF problem of the group I is solved once for all instead of for one angular momentum l each time.

A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

Decay of resonant states and determination of their quantum numbers

1970 ◽  
Vol 101 (8) ◽  
pp. 655-696 ◽  
Author(s):  
M.S. Dubovikov ◽  
Yurii A. Simonov
Keyword(s):  
Quantum Numbers ◽  
Resonant States

Temperature Dependences in the O + OH → O2 + H Reaction. Quasiclassical Trajectory Calculation

1993 ◽  
Vol 58 (2) ◽  
pp. 234-243 ◽  
Author(s):  
Viliam Klimo ◽  
Martina Bittererová ◽  
Stanislav Biskupič ◽  
Ján Urban ◽  
Miroslav Micov
Keyword(s):  
Temperature Dependence ◽  
Energy Surface ◽  
Analytical Form ◽  
Mean Values ◽  
Quantum Numbers ◽  
Mean Lifetime ◽  
Temperature Dependences ◽  
Quasiclassical Trajectory Calculation ◽  
The Mean ◽  
Combustion Processes

The reaction O + OH → O2 + H in conditions of combustion of hydrocarbons and polymers was modelled by using the method of quasiclassical trajectories. The potential energy surface was determined by the multiconfiguration interaction method and fitted with the analytical form of the extended LEPS function. Attention was paid to the mean values of the vibrational and rotational quantum numbers of O2 molecules and their temperature dependence. The temperature dependence of the mean lifetime of the OOH collision complex was also examined. The calculated rate constants were analyzed and compared with the experimental data over the temperature region of the combustion processes.

Quantum Theory

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Uncertainty Principle ◽  
Quantum Spin ◽  
Quantum States ◽  
Wave Functions ◽  
Symbolic Representations ◽  
Quantum Numbers ◽  
The Subject ◽  
Heisenberg's Uncertainty Principle

The subject of Chapter 8 is the fundamental principles of quantum theory, the abstract extension of quantum mechanics. Two of the entities explored are kets and operators, with kets being representations of quantum states as well as a source of wave functions. The quantum box and quantum spin kets are specified, as are the quantum numbers that identify them. Operators are introduced and defined in part as the symbolic representations of observable quantities such as position, momentum and quantum spin. Eigenvalues and eigenkets are defined and discussed, with the former identified as the possible outcomes of a measurement. Bras, the counterpart to kets, are introduced as the means of forming probability amplitudes from kets. Products of operators are examined, as is their role underpinning Heisenberg’s Uncertainty Principle. A variety of symbol manipulations are presented. How measurements are believed to collapse linear superpositions to one term of the sum is explored.

scholarly journals Leptonic Dirac CP violation predictions from residual discrete symmetries

2016 ◽  
Vol 902 ◽  
pp. 1-57 ◽  
Author(s):  
I. Girardi ◽  
S.T. Petcov ◽  
Alexander J. Stuart ◽  
A.V. Titov
Keyword(s):  
Cp Violation ◽  
Discrete Symmetries

scholarly journals KLT factorization of winding string amplitudes

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Jaume Gomis ◽  
Ziqi Yan ◽  
Matthew Yu
Keyword(s):  
Scattering Amplitudes ◽  
Open String ◽  
Closed String ◽  
Open Strings ◽  
Toroidal Compactifications ◽  
Quantum Numbers ◽  
String Amplitudes

Abstract We uncover a Kawai-Lewellen-Tye (KLT)-type factorization of closed string amplitudes into open string amplitudes for closed string states carrying winding and momentum in toroidal compactifications. The winding and momentum closed string quantum numbers map respectively to the integer and fractional winding quantum numbers of open strings ending on a D-brane array localized in the compactified directions. The closed string amplitudes factorize into products of open string scattering amplitudes with the open strings ending on a D-brane configuration determined by closed string data.

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