《METHODS IN COMPUTATIONAL PHYSICS Volume 2 Quantum Mechanics》

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METHODS IN COMPUTATIONAL PHYSICS Volume 2 Quantum Mechanics PDF电子版封面

THE GAUSSIAN FUNCTION IN CALCULATIONS OF STATISTICAL MECHANICS AND QUANTUM MECHANICS＆Isaiah Shavitt1

Ⅰ．Introduction1

Ⅱ．Some Properties of the Gsussian Function2

Ⅲ．A Problem in Statistical Mechanics:Virial Coefficients16

Ⅳ．A Problem in Quantum Mechanics:Multicenter Integrals27

References44

ATOMIC SELF-CONSISTENT FIELD CALCULATIONS BY THE EXPANSION METHOD＆C．C．f．Roothaan and P．S．Bagus47

Ⅰ．Introduction47

Ⅱ．General Theory49

Ⅲ．Calculation of Integrals55

Ⅳ．Eigenvectors and Eigenvalues57

Ⅴ．SCF Iterations and Extrapolations62

Ⅵ．Convergence Control64

Ⅶ．Exponent Variation67

Ⅷ．Output Format and Options73

Ⅸ．Input Format and Conventions76

Ⅹ．Limitations of the Program93

References94

THE EVALUATION OF MOLECULAR INTEGRALS BY THE ZETA-FUNCTION EXPANSION＆M．P．Barnett95

Ⅰ．Introduction95

Ⅱ．The Zeta Function Expansion97

Ⅲ．Two-Center One Electron Integrals101

Ⅳ．Two-Center Coulomb and Hybrid Integrals108

Ⅴ．Three-Center One Electron Integrals113

Ⅵ．Three-Center Coulomb Integrals120

Ⅶ．Two-and Three-Center Exchange Integrals124

Ⅷ．Four-Center Integrals128

Ⅸ．Analytical and Numerical Methods141

Ⅹ．Coding Methods146

References152

INTEGRALS FOR DIATOMIC MOLECULAR CALCULATIONS＆Fernando J．Corbató and Alfred C．Switendick155

Ⅰ．Introduction155

Ⅱ．Formulation156

Ⅲ．Organization164

Ⅳ．Generation of β Functions167

Ⅴ．Generation of D Coefficients170

Ⅵ．Numerical Quadrature174

Ⅶ．Exclusion of Redundant Integrals176

References178

NONSEPARABLE THEORY OF ELECTRON-HYDROGEN SCATTERING＆A．Temkin and D．E．Hoover181

Ⅰ．Introduction181

Ⅱ．Reduction of the S-Wave Equation185

Ⅲ．Solution of the Zeroth-Order Problem190

Ⅳ．Calculation of the Higher Order Terms216

Ⅴ．Results and Discussion230

Appendix Ⅰ237

Appendix Ⅱ239

References240

ESTIMATING CONVERGENCE RATES OF VARIATIONAL CALCULATIONS＆Charles Schwartz241

Ⅰ．Introduction241

Ⅱ．Model Problems:Integrated Least-Square Fitting of Functions244

Ⅲ．The Real Problems:Variational Approximations to Solutions of Schrodinger＇s Equation251

Ⅳ．Examples254

Ⅴ．Further Calculations on the Two-Electron Atom:The l-Expansion in the Angle262

Ⅵ．Concluding Remarks265

References266

AUTHOR INDEX267

SUBJECT INDEX269

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