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Microcomputer quantum mechanics

Author: J P Killingbeck
Publisher: Boca Raton, FL : CRC Press, 2018.
Series: CRC revivals.
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
Summary:
"Microcomputer Quantum Mechanics combines the teaching of computing skills with depth of mathematical understanding. This practical text demonstrates how computation can be integrated with theoretical analysis as part of a unified attack on problems in one of the most interesting areas of modern physics. The author discusses the mathematical principles behind the programs and actually creates new methods to  Read more...
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Details

Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: J P Killingbeck
ISBN: 1351083031 9781351083034 9781351074582 135107458X 9781351083041 135108304X 9781351099936 1351099930
OCLC Number: 1020633621
Notes: Includes index.
Description: 1 online resource.
Contents: Cover; Half Title; Title; Copyright; Contents; Preface to the second edition; Preface to the first edition; 1: Microcomputers and BASIC; 1.1: What is a microcomputer?; 1.2: Interaction and iteration; 1.3: Theory in action; 1.4: Varieties of BASIC; Exercises; solutions; 1.5: Flow charts; Notes; 2: Tuning the instrument; 2.1: General comments; 2.2: Significant figures tests; 2.3: Some speed tests; 2.4: Subroutines; 2.5: Labour-saving analysis; Exercises; solutions; 3: The iterative approach; 3.1: Introduction; 3.2: The input-output approach; 3.3: Newton's method. 3.4: Iterative calculation of inverses3.5: The Gauss-Seidel method; 3.6: Matrix eigenvalues by iteration; 3.7: Matrix folding; Exercise; solutions; notes; 4: Some finite-difference methods; 4.1: Introduction; 4.2: The Newton-Gregory formula; 4.3: Derivatives and Richardson extrapolation; Exercises; solutions; 5: Numerical integration; 5.1: Introduction; 5.2: A simple test integral; 5.3: A Taylor series approach; 5.4: Romberg integration; 5.5: Change of variable; 5.6: Numerical differentiation; 5.7: Endpoint singularities; 5.8: Multiple integrals; Exercises; solutions; notes. 6: Padé approximants and all that6.1: Power series and their uses; 6.2: Series of Stieltjes; 6.3: Padé approximants; 6.4: Computing Padé approximants; Exercises; solutions; notes; 7: A simple power series method; 7.1: Introduction; 7.2: Standard forms of the SchrÃœdinger equation; 7.3: Some interesting test cases; 7.4: The power series approach; Exercises; solutions; notes; 8: Some matrix calculations; 8.1: Introduction; 8.2: Matrices in quantum mechanics; 8.3: The Hill determinant approach; 8.4: Other types of eigenvalue calculation; Notes; 9: Hypervirial-perturbation methods. 9.1: Introduction9.2: Rayleigh-SchrÃœdinger theory; 9.3: The Hylleraas principle for E2; 9.4: The expectation value problem; 9.5: Calculating Ï#x88;(0) for radial problems; 9.6: Hypervirial relations; 9.7: Renormalised perturbation series; 9.8: The sum-over-states formalism; Exercises; solutions; notes; 10: Finite-difference eigenvalue calculations; 10.1: Introduction; 10.2: The one-dimensional equation; 10.3: A perturbation approach; 10.4: Some numerical results; 10.5: Numerov's method; 10.6: The radial equation; 10.7: Further applications; Exercises; solutions; notes. 11: One-dimensional model problems11.1: Introduction; 11.2: A one-dimensional molecule; 11.3: A one-dimensional band problem; 12: Some case studies; 12.1: Introduction; 12.2: A simple helium atom calculation; 12.3: Monte-Carlo optimisation; 12.4: The charmonium problem; 12.5: The quadratic Zeeman effect; 12.6: Quasi-bound states; Notes; 13: Some recent developments; 13.1: Introduction; 13.2: Recent mathematical work; 13.3: Comments on selected microcomputers; 13.4: The inner product method; Notes; Appendices; Appendix 1: Useful mathematical identities.
Series Title: CRC revivals.
Responsibility: edited by J.P. Killingbeck.

Abstract:

"Microcomputer Quantum Mechanics combines the teaching of computing skills with depth of mathematical understanding. This practical text demonstrates how computation can be integrated with theoretical analysis as part of a unified attack on problems in one of the most interesting areas of modern physics. The author discusses the mathematical principles behind the programs and actually creates new methods to facilitate the application of microcomputers in quantum mechanics. Microcomputer Quantum Mechanics combines the teaching of computing skills with depth of mathematical understanding. This practical text demonstrates how computation can be integrated with theoretical analysis as part of a unified attack on problems in one of the most interesting areas of modern physics. The author discusses the mathematical principles behind the programs and actually creates new methods to facilitate the application of microcomputers in quantum mechanics."--Provided by publisher.

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