Method of recurrent construction of Löwdin spin-adapted wave functions. III. Löwdin basis and its permutation symmetry: Evaluation of overlap integrals

1983 ◽  
Vol 24 (3) ◽  
pp. 279-306 ◽  
Author(s):  
A. I. Panin
Keyword(s):  
Wave Functions ◽  
Overlap Integrals ◽  
Permutation Symmetry

scholarly journals Symmetries in subatomic multi-quark systems

2018 ◽  
Vol 27 (12) ◽  
pp. 1840003
Author(s):  
J. D. Vergados ◽  
D. Strottman
Keyword(s):  
Quantum Chromodynamics ◽  
Quark Model ◽  
Spin Symmetry ◽  
Wave Functions ◽  
Low Energy ◽  
Isospin Symmetry ◽  
Permutation Symmetry

We discus the role of Quantum Chromodynamics (QCD) in low energy phenomena involving the color-spin symmetry of the quark model. We then combine it with orbital and isospin symmetry to obtain wave functions with the proper permutation symmetry, focusing on multi-quark systems.

Permutation Symmetry of Many-Particle Wave Functions

1965 ◽  
Vol 139 (2B) ◽  
pp. B500-B508 ◽  
Author(s):  
M. D. Girardeau
Keyword(s):  
Wave Functions ◽  
Permutation Symmetry

One-dimensional overlap functions and their application to Auger recombination in semiconductors

1960 ◽  
Vol 258 (1295) ◽  
pp. 486-495 ◽  
Keyword(s):  
Auger Recombination ◽  
Elevated Temperatures ◽  
Bloch Wave ◽  
Wave Functions ◽  
General Analysis ◽  
Experimental Results ◽  
Overlap Integrals ◽  
Recombination Mechanism ◽  
One Dimensional ◽  
Good Agreement

The theoretical lifetime of excess carriers in semiconductors limited only by the Auger recombination mechanism previously discussed by the present authors, depends on a temperature-independent parameter. This involves certain overlap integrals. They are of the form ∫ u *(k 1 , r) u (k 2 , r) dr, where the u ’s are the modulating parts of Bloch wave functions. The integrals are calculated in this paper on the basis of a Kronig-Penney model. The value of the parameter obtained is shown to be rather insensitive to many details of the model used. When the value found is inserted into the previously published theory of lifetimes in InSb, very good agreement is obtained with the more detailed experimental results which have recently become available. This strongly suggests that the dominant recombination mechanism in InSb at elevated temperatures has been identified. A more general analysis of the properties of the overlap integrals is also given in this paper.

scholarly journals Cyclopentadienyl System: Solving the Secular Determinant, π Energy, Delocalization Energy, Wave Functions, Electron Density and Charge Density

2020 ◽  
Vol 6 (2) ◽  
Author(s):  
Vikram R. Jadhav ◽  
Jamdhade Madhuri ◽  
Wadhawane Pooja ◽  
Y.R. Baste
Keyword(s):  
Charge Density ◽  
Electron Density ◽  
Wave Functions ◽  
Stable Configuration ◽  
Overlap Integrals ◽  
Delocalization Energy ◽  
Study Characteristics ◽  
Secular Equations ◽  
Coulomb Integrals ◽  
Secular Determinant

In this study, characteristics of Hückel strategy, were abused so as to acquire some significant outcomes, through a theoretical technique with which it is conceivable to get secular equations, π energy, wave functions, electron density and charge density, as an account of cyclopentadienyl system i.e. C5H5+ (cation), C5H5- (anion), and C5H5. (radical) and permitting the expression of delocalization energy of conjugated cyclopentadienyl ring framework. Here, it was presented the secular determinant of the Hückel technique and applied to cyclopentadienyl system framework so as to communicate their orbital energies of cyclopentadienyl system, also to communicate its electron and charge density in terms of stable configuration of a system. It is settled by the Hückel strategy and applied by the assumptions for nearby comparability such as coulomb integrals, exchange integrals and overlap integrals. This simple way hypothetical strategy will allow to graduate and post graduate understudies to understanding the investigation of stable configuration, electron and charge density and also other parameters.

scholarly journals Recoupling mechanism for exotic mesons and baryons

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yu. A. Simonov
Keyword(s):  
Bound States ◽  
Wave Functions ◽  
Infinite Chain ◽  
Explicit Calculation ◽  
Overlap Integrals ◽  
Channel Coupling ◽  
Exotic Mesons ◽  
Narrow Peak

Abstract The infinite chain of transitions of one pair of mesons (channel I) into another pair of mesons (channel II) can produce bound states and resonances in both channels even if no interactions inside channels exist. These resonances which can occur also in meson-baryon channels are called channel-coupling (CC) resonances. A new mechanism of CC resonances is proposed where transitions occur due to a rearrangement of confining strings inside each channel — the recoupling mechanism. The amplitude of this recoupling mechanism is expressed via overlap integrals of the wave functions of participating mesons (baryons). The explicit calculation with the known wave functions yields the peak at E = 4.12 GeV for the transitions $$ J/\psi +\phi \leftrightarrow {D}_s^{\ast }+{\overline{D}}_s^{\ast } $$ J / ψ + ϕ ↔ D s ∗ + D ¯ s ∗ , which can be associated with χc1 (4140), and a narrow peak at 3.98 GeV with the width 10 MeV for the transitions $$ {D}_s^{-}+{D}_0^{\ast}\leftrightarrow J/\psi +{K}^{\ast -} $$ D s − + D 0 ∗ ↔ J / ψ + K ∗ − , which can be associated with th recently discovered Zcs (3985).

Molecular Vibrations in the Exciton Theory for Molecular Aggregates. I. General Theory

1961 ◽  
Vol 14 (3) ◽  
pp. 329 ◽  
Author(s):  
EG McRae
Keyword(s):  
Wave Functions ◽  
Harmonic Oscillators ◽  
Overlap Integrals ◽  
Molecular Aggregate ◽  
Individual Wave ◽  
Electronically Excited ◽  
Ordered Array ◽  
Vibronic States ◽  
Sums Of Products ◽  
Explicit Expressions

A molecular aggregate is defined as an ordered array of identical molecules. This definition includes molecular crystals, dimers, and certain polymeric aggregates of dye molecules. The vibronic states of an electronically excited molecular aggregate are studied theoretically. The aggregate is treated as an array of non-rigid molecules in a rigid lattice. The simplest form of the exciton theory is assumed to be correct except with regard to intramolecular vibrations. The molecules in the aggregate are considered as harmonic oscillators with one vibrational degree of freedom, whose individual wave functions are Born-Oppenheimer separable. The molecules are assumed to interact by a purely electronic mechanism. Born-Oppenheimer separable wave functions for the whole aggregate, here called E-V functions, are defined. It is shown that the interaction integrals between E-V functions may be expressed in terms of integrals which depend only on the properties of individual molecules. Explicit expressions are given for the latter integrals. The resonance interactions between E-V functions are described. On this basis, the limiting conditions under which the E-V functions steadily approach exact vibronic state functions of the aggregate are specified. The vibrational overlap integrals between E-V and electronic ground-state wave functions are studied. These integrals may be expressed as sums of products of vibrational overlap integrals for individual molecules. Explicit expressions for the latter integrals are obtained through an approximation to Hutchisson's theory.

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