Author 
Avery, John, 1933

Subject 
Algebras, Linear.


Symmetry (Physics)


Basis sets (Quantum mechanics)

Alt Name 
Rettrup, Sten.


Avery, James.

Description 
1 online resource (xi, 227 pages) : illustrations 
Bibliography Note 
Includes bibliographical references (pages 207219) and index. 
Contents 
1. General considerations. 1.1 The need for symmetryadapted basis functions. 1.2. Fundamental concepts. 1.3 Definition of invariant blocks. 1.4. Diagonalization of the invariant blocks. 1.5. Transformation of the large matrix to blockdiagonal form. 1.6. Summary of the method  2. Examples from atomic physics. 2.1. The HartreeFockRoothaan method for calculating atomic orbitals. 2.2. Automatic generation of symmetryadapted configurations. 2.3. RussellSaunders states. 2.4. Some illustrative examples. 2.5. The SlaterCondon rules. 2.6. Diagonalization of invariant blocks using the SlaterCondon rules  3. Examples from quantum chemistry. 3.1. The HartreeFockRoothaan method applied to molecules. 3.2. Construction of invariant subsets. 3.3. The trigonal group C[symbol] the NH[symbol] molecule  4. Generalized sturmians applied to atoms. 4.1. Goscinskian configurations. 4.2. Relativistic corrections. 4.3. The largeZ approximation: restriction of the basis set to an Rblock. 4.4. Electronic potential at the nucleus in the largeZ approximation. 4.5. Core ionization energies. 4.6. Advantages and disadvantages of Goscinskian configurations. 4.7. Rblocks, invariant subsets and invariant blocks. 4.8. Invariant subsets based on subshells; Classification according to M[symbol] and M[symbol]. 4.9. An atom surrounded by point charges  5. Molecular orbitals based on sturmians. 5.1. The oneelectron secular equation. 5.2. ShibuyaWulfman integrals and Sturmian overlap integrals evaluated in terms of hyperpherical harmonics. 5.3. Molecular calculations using the isoenergetic configurations. 5.4. Building T[symbol] and [symbol] from 1electron components. 5.5. Interelectron repulsion integrals for molecular Sturmians from hyperspherical harmonics. 5.6. Manycenter integrals treated by Gaussian expansions (Appendix E). 5.7. A pilot calculation. 5.8. Automatic generation of symmetryadapted basis functions  6. An example from acoustics. 6.1. The Helmholtz equation for a nonuniform medium. 6.2. Homogeneous boundary conditions at the surface of a cube. 6.3. Spherical symmetry of v(x); nonseparability of the Helmholtz equation. 6.4. Diagonalization of invariant blocks  7. An example from heat conduction. 7.1. Inhomogeneous media . 7.2. A 1dimensional example. 7.3. Heat conduction in a 3dimensional inhomogeneous medium  8. Symmetryadapted solutions by iteration. 8.1. Conservation of symmetry under Fourier transformation. 8.2. The operator [symbol] and its Green's function. 8.3. Conservation of symmetry under iteration of the Schrodinger equation. 8.4. Evaluation of the integrals. 8.5. Generation of symmetryadapted basis functions by iteration. 8.6. A simple example. 8.7. An alternative expansion of the Green's function that applies to the Hamiltonian formulation of physics. 
Summary 
In theoretical physics, theoretical chemistry and engineering, one often wishes to solve partial differential equations subject to a set of boundary conditions. This gives rise to eigenvalue problems of which some solutions may be very difficult to find. For example, the problem of finding eigenfunctions and eigenvalues for the Hamiltonian of a manyparticle system is usually so difficult that it requires approximate methods, the most common of which is expansion of the eigenfunctions in terms of basis functions that obey the boundary conditions of the problem. The computational effort needed in such problems can be much reduced by making use of symmetryadapted basis functions. The conventional method for generating symmetryadapted basis sets is through the application of group theory, but this can be difficult. This book describes an easier method for generating symmetryadapted basis sets automatically with computer techniques. The method has a wide range of applicability and can be used to solve difficult eigenvalue problems in a number of fields. The book is of special interest to quantum theorists, computer scientists, computational chemists and applied mathematicians. 
ISBN 
9814350478 (electronic bk.) 

9789814350471 (electronic bk.) 

9789814350464 

981435046X 
OCLC # 
776990543 
Additional Format 
Print version: 9789814350464 981435046X 
