Electronic wave functions - The evaluation of the general vector-coupling coefficients by automatic computation

1954 ◽  
Vol 246 (917) ◽  
pp. 463-479 ◽  
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Coupling Coefficients ◽  
Easy Method ◽  
Atomic Wave Function ◽  
Vector Coupling ◽  
Method Of Calculation ◽  
Different Types ◽  
Function Calculation ◽  
Method Of Evaluation

A considerable number of different types of investigations on atomic and nuclear wave functions involve the use of vector-coupled functions and would be facilitated by an easy method of evaluation of the basic fundamental coefficients. This is particularly so for the present series of investigations, in which very complicated vector-coupled functions are used in convergent methods of atomic wave-function calculation. Hitherto the evaluation of these coefficients, which are independent of all aspects of a problem other than the irreducible representations of the rotational group concerned, has been extremely tedious while still requiring considerable mathematical understanding. It has now been found possible to develop a method of calculation which can be performed purely automatically by the EDSAC, proceeding from the lowest argument values indefinitely through all higher values. A substantial table, which would otherwise require over a year of computation by a mathematician, has been obtained. This investigation constitutes a significant contribution to problems of wave-function calculation and also involves some minor innovations in the vector-coupling theory.

Electronic wave functions: VI. Some theorems facilitating the evaluation of Schrödinger integrals of vector-coupled functions

1952 ◽  
Vol 245 (893) ◽  
pp. 95-115 ◽  
Keyword(s):  
General Theory ◽  
Wave Functions ◽  
Coupling Coefficients ◽  
Restricted Class ◽  
Vector Coupling ◽  
Electronic Wave ◽  
Atomic Wave ◽  
Variational Calculations ◽  
Electronic Wave Functions

The theorems reported here provide some powerful additional relations to the general theory of the reduction of Schrodinger integrals completed in part V. One result of these is to establish a number of relations between the various vector-coupling coefficients and thus to reduce considerably the labour of calculation of these. A second result is to provide a method of evaluating the two-electron electrostatic integrals which is a complete alternative to the c k method which has generally been used previously. This appears to be simpler and more powerful. A third result is only applicable to a restricted class of integrals and only to particular terms in the formulas for these, but where applicable it makes trivial the evaluation of the terms concerned and actually simplifies about three-quarters of the integrals normally occurring. These methods have been found to be extremely useful in the convergent variational calculations of atomic wave functions, and will also be applicable to all problems which require the evaluation of Schrödinger integrals between vector-coupled functions.

scholarly journals Modern methods of evaluation existing suppliers and suppliers selected by customer for small and medium-sized companies

2010 ◽  
Vol 58 (6) ◽  
pp. 199-208 ◽  
Author(s):  
Marie Jurová ◽  
Ekaterina Sutormina
Keyword(s):  
Theoretical Method ◽  
Global Market ◽  
Universal Method ◽  
Delivery Time ◽  
Universal System ◽  
Method Of Calculation ◽  
Evaluative Criteria ◽  
Methods Of Evaluation ◽  
Different Types ◽  
Method Of Evaluation

On existing conditions on global market (almost identical quality, almost identical purchasing values) companies have to definite the total rating of importance of evaluative criteria. In post-crisis period the problem of suppliers’ evaluation is one of the biggest, because companies had to use all resources and all possibilities to develop their own business. Many authors wrote about collaborative planning and warehousing as one of possibilities to optimization work inside supply chain. For this paper define small and medium-sized enterprises (SME) as enterprises with the size of maximum 250 em­ployers. In literature was read we couldn’t find information about own system of suppliers evaluation for small and medium-sized enterprises. SME can have some different types of business and in this case need the universal system of eva­lua­tion. The research of this paper is oriented on small and medium-sized enterprises with different types of business. The new theoretical universal method of calculation for evaluation existing suppliers for small and medium-sized enterprises will present in this paper. This theoretical method is based on average values. This method includes traditional evaluative criteria (quality, delivery time) and other (mobility of supplier, possibilities of new level of partnership). This method of evaluation can not be used for continual manufacture. New method can improve the total evaluation of supplier in small and medium-sized enterprises.

Gravity as the curvature of the wave function of the universe.

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Main Task ◽  
Reference Systems ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Principle Of Equivalence ◽  
Relative Wave Function ◽  
New Equation ◽  
The Universe

Modern general theory of relativity considers gravity as the curvature of space-time. The theory is based on the principle of equivalence. All bodies fall with the same acceleration in the gravitational field, which is equivalent to locally accelerated reference systems. In this article, we will affirm the concept of gravity as the curvature of the relative wave function of the Universe. That is, a change in the phase of the universal wave function of the Universe near a massive body leads to a change in all other wave functions of bodies. The main task is to find the form of the relative wave function of the Universe, as well as a new equation of gravity for connecting the curvature of the wave function and the density of matter.

scholarly journals OnSU 3 vector coupling coefficients

1966 ◽  
Vol 41 (4) ◽  
pp. 639-639
Author(s):  
G. Ponzano
Keyword(s):  
Coupling Coefficients ◽  
Vector Coupling

The electrostatic calculation of molecular energies - IV. Optimum paired-electron orbitals and the electrostatic method

1956 ◽  
Vol 235 (1201) ◽  
pp. 224-234 ◽  
Keyword(s):  
Simple Procedure ◽  
Wave Functions ◽  
Optimum Form ◽  
Method Of Calculation ◽  
Hartree Fock ◽  
Electron Orbital ◽  
Electrostatic Method ◽  
Valence States ◽  
Paired Electron ◽  
Electrostatic Interpretation

Equations which determine the optimum form of paired-electron orbitals are derived. It is shown that for large nuclear separations these equations become the Hartree-Fock equa­tions for appropriate valence states of the separated atoms. An electrostatic interpretation of chemical bonding is developed using optimum paired-electron orbital functions. For these wave functions this simple procedure yields results identical with those obtained by the conventional method of calculation based on the Hamiltonian integral. Numerical computations by the electrostatic method are also discussed.

scholarly journals INTEGRAL TRANSFORM TECHNIQUE FOR MESON WAVE FUNCTIONS

1996 ◽  
Vol 11 (20) ◽  
pp. 1611-1626 ◽  
Author(s):  
A.P. BAKULEV ◽  
S.V. MIKHAILOV
Keyword(s):  
Wave Function ◽  
Sum Rules ◽  
Integral Transform ◽  
Wave Functions ◽  
Sum Rule ◽  
New Approach ◽  
Exactly Solvable ◽  
The Stability ◽  
The Masses ◽  
Integral Transform Technique

In a recent paper1 we have proposed a new approach for extracting the wave function of the π-meson φπ(x) and the masses and wave functions of its first resonances from the new QCD sum rules for nondiagonal correlators obtained in Ref. 2. Here, we test our approach using an exactly solvable toy model as illustration. We demonstrate the validity of the method and suggest a pure algebraic procedure for extracting the masses and wave functions relating to the case under investigation. We also explore the stability of the procedure under perturbations of the theoretical part of the sum rule. In application to the pion case, this results not only in the mass and wave function of the first resonance (π′), but also in the estimation of π″-mass.

The Wave Theory of the Electron

1928 ◽  
Vol 24 (4) ◽  
pp. 501-505 ◽  
Author(s):  
J. M. Whittaker
Keyword(s):  
Wave Function ◽  
Differential Equations ◽  
Fourth Order ◽  
Commutative Algebra ◽  
Wave Theory ◽  
Wave Functions ◽  
Linear Differential Equations ◽  
Wave Mechanics ◽  
First Order ◽  
Linear Differential

In two recent papers Dirac has shown how the “duplexity” phenomena of the atom can be accounted for without recourse to the hypothesis of the spinning electron. The investigation is carried out by the methods of non-commutative algebra, the wave function ψ being a matrix of the fourth order. An alternative presentation of the theory, using the methods of wave mechanics, has been given by Darwin. The four-rowed matrix ψ is replaced by four wave functions ψ1, ψ2, ψ3, ψ4 satisfying four linear differential equations of the first order. These functions are related to one particular direction, and the work can only be given invariance of form at the expense of much additional complication, the four wave functions being replaced by sixteen.

LONG RANGE FORCES BETWEEN HYDROGEN MOLECULES

1955 ◽  
Vol 33 (11) ◽  
pp. 668-678 ◽  
Author(s):  
F. R. Britton ◽  
D. T. W. Bean
Keyword(s):  
Wave Function ◽  
Long Range ◽  
Ground State ◽  
Close Agreement ◽  
Van Der Waals ◽  
Wave Functions ◽  
Numerical Factor ◽  
Hydrogen Molecules ◽  
Static Quadrupole

Long range forces between two hydrogen molecules are calculated by using methods developed by Massey and Buckingham. Several terms omitted by them and a corrected numerical factor greatly change results for the van der Waals energy but do not affect their results for the static quadrupole–quadrupole energy. By using seven approximate ground state H2 wave functions information is obtained regarding the dependence of the van der Waals energy on the choice of wave function. The value of this energy averaged over all orientations of the molecular axes is found to be approximately −11.0 R−6 atomic units, a result in close agreement with semiempirical values.

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