Ebook: The Recursion Method and Its Applications: Proceedings of the Conference, Imperial College, London, England September 13–14, 1984
- Tags: Mathematical Methods in Physics, Numerical and Computational Physics, Condensed Matter Physics
- Series: Springer Series in Solid-State Sciences 58
- Year: 1985
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
This volume reviews recent advances in the development and application of the recursion method in computational solid state physics and elsewhere. It comprises the invited papers which were presented at a two-day conference at Imperial College, London during September 1984. The recursion method is based on the Lanczos algorithm for the tridiago nalisation of matrices, but it is much more than a straightforward numerical technique. It is widely regarded as the most elegant framework for a variety of calculations into which one may incorporate physical insights and a num ber of technical devices. The standard reference is Volume 35 of Solid State Physics, which contains all the early ideas of Heine, Haydock and others, upon which the method was established. The present volume provides the first review of subsequent developments. It also indicates where problems remain, or opinions differ, in the interpretation of the mathematical details or choice of practical techniques in applications. The field is still very li vely and much remains to be done, as the summary chapter clearly demonstra tes. We are grateful to the S. E. R. C. 's Collaborative Computational Project No. 9 on the electronic structure of solids and the Institute of Physics's Solid State Sub-committee for their sponsorship of the conference. We thank Angus MacKinnon for his help in conference organisation and Jacyntha Crawley for secretarial assistance. December 1984 David G. Pettifor Denis L. Weaire v Contents Part I Introduction Why Recur? By V.
Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-1
Why Recur?....Pages 2-7
The Recursive Solution of Schroedinger’s Equation....Pages 8-20
Front Matter....Pages 21-21
Asymptotic Behaviour of Continued Fraction Coefficients Related to Singularities of the Weight Function....Pages 22-45
Band Gaps and Asymptotic Behaviour of Continued Fraction Coefficients....Pages 46-51
Computing Greenians: Quadrature and Termination....Pages 52-60
Application of Linear Prediction for Extrapolating Recursion Coefficients....Pages 61-69
Front Matter....Pages 71-71
On a Generalized-Moments Method....Pages 72-83
The Equation of Motion Method....Pages 84-90
Use of Cyclic Matrices to Obtain Analytic Expressions for Crystals....Pages 91-101
Front Matter....Pages 103-103
Continued Fractions and Perturbation Theory: Application to Tight Binding Systems....Pages 104-119
Response Functions and Interatomic Forces....Pages 120-131
The Recursion Method with a Non-Orthogonal Basis....Pages 132-137
Front Matter....Pages 139-139
Hamiltonian Eigenvalues for Lattice Gauge Theories....Pages 140-148
The Lanczos Method in Lattice Gauge Theories....Pages 149-164
A Dedicated Lanczos Computer for Nuclear Structure Calculations....Pages 165-169
Front Matter....Pages 171-171
Conference Summary....Pages 172-177
Back Matter....Pages 179-183
Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-1
Why Recur?....Pages 2-7
The Recursive Solution of Schroedinger’s Equation....Pages 8-20
Front Matter....Pages 21-21
Asymptotic Behaviour of Continued Fraction Coefficients Related to Singularities of the Weight Function....Pages 22-45
Band Gaps and Asymptotic Behaviour of Continued Fraction Coefficients....Pages 46-51
Computing Greenians: Quadrature and Termination....Pages 52-60
Application of Linear Prediction for Extrapolating Recursion Coefficients....Pages 61-69
Front Matter....Pages 71-71
On a Generalized-Moments Method....Pages 72-83
The Equation of Motion Method....Pages 84-90
Use of Cyclic Matrices to Obtain Analytic Expressions for Crystals....Pages 91-101
Front Matter....Pages 103-103
Continued Fractions and Perturbation Theory: Application to Tight Binding Systems....Pages 104-119
Response Functions and Interatomic Forces....Pages 120-131
The Recursion Method with a Non-Orthogonal Basis....Pages 132-137
Front Matter....Pages 139-139
Hamiltonian Eigenvalues for Lattice Gauge Theories....Pages 140-148
The Lanczos Method in Lattice Gauge Theories....Pages 149-164
A Dedicated Lanczos Computer for Nuclear Structure Calculations....Pages 165-169
Front Matter....Pages 171-171
Conference Summary....Pages 172-177
Back Matter....Pages 179-183
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