1 (p1): 1．INTRODUCTION
1 (p1-1): 1．1．SEVEN STEPS IN THE DEVELOPMENT OF ATOMIC THEORY
2 (p1-2): 1．2．WHY CALCULATE ATOMIC STRUCTURES?
3 (p1-3): 1．3．ATOM AND SOLAR SYSTEM
5 (p1-4): 1．4．ATOMIC UNITS
6 (p1-5): 1．5．SCHRODINGER＇S EQUATION FOR AN ELECTRON
8 (p1-6): 1．6．CENTRAL-FIELD WAVE FUNCTIONS
11 (p1-7): 1．7．ELECTRON SPIN
13 (p1-8): 1．8．MANY-PARTICLE SYSTEMS IN WAVE MECHANICS
16 (p1-8-1): 1．8．1．The necessity for approximation in calculations of atomic structure
17 (p1-9): 1．9．THE SEPARABLE WAVE FUNCTION APPROXIMATION
22 (p2): 2．THE VARIATION PRINCIPLE
22 (p2-1): 2．1．STATIONARY STATES OF A PARTICLE IN ONE DIMENSION
26 (p2-1-1): 2．1．1．E＇ as a Lagrange multiplier
27 (p2-2): 2．2．PARTICLE IN THREE DIMENSIONS
29 (p2-3): 2．3．MANY-PARTICLE SYSTEMS,IN COORDINATE SPACE
30 (p2-4): 2．4．TWO WAYS OF USING THE VARIATION PRINCIPLE TO DERIVE APPROXIMATE WAVE FUNCTIONS
31 (p2-5): 2．5．THE SEPARABLE WAVE FUNCTION APPROXIMATION FOR THE NORMAL STATE OF HELIUM
36 (p2-6): 2．6．THE VARIATION PRINCIPLE FOR EXCITED STATES
37 (p2-7): 2．7．ANALYTIC WAVE FUNCTIONS
39 (p3): 3．CONFIGURATIONS OF COMPLETE GROUPS
39 (p3-1): 3．1．THREE STAGES IN THE CALCULATION OF ATOMIC STRUCTURES
39 (p3-2): 3．2．ALGEBRAICAL PRELIMINARIES TO THE MANIPULATION OF DETERMINANT WAVE FUNCTIONS
42 (p3-3): 3．3．FIRST STAGE;DERIVATION OF THE EXPRESSION FOR E＇
45 (p3-4): 3．4．USE OF CENTRAL-FIELD WAVE FUNCTIONS
50 (p3-5): 3．5．THE Yk AND Zk FUNCTIONS
52 (p3-6): 3．6．SECOND STAGE:APPLICATION OF THE VARIATION PRINCIPLE
55 (p3-6-1): 3．6．1．Equations for the normal configuration of a ten-electron system
57 (p3-7): 3．7．FOCK＇S EQUATIONS AS INTEGRODIFFERENTIAL EQUATIONS
58 (p3-8): 3．8．THE NONDIAGONAL ε PARAMETERS
59 (p3-9): 3．9．EQUATIONS WITHOUT EXCHANGE
60 (p3-9-1): 3．9．1．Slater＇s simplified form of the equations with exchange
63 (p4): 4．NUMERICAL PROCEDURES
63 (p4-1): 4．1．FINITE DIFFERENCES
64 (p4-2): 4．2．THE MAIN FORMULAE IN FINITE DIFFERENCES
65 (p4-3): 4．3．QUADRATURE
68 (p4-4): 4．4．SECOND-0ORDER DIFFERENTIAL EQUATION WITH FIRST DERIVATIVE ABSENT
71 (p4-5): 4．5．NUMEROV＇S PROCESS FOR A LINEAR SECOND-ORDER EQUATION
72 (p4-6): 4．6．FIRST-ORDER EQUATIONS
73 (p4-7): 4．7．FOX-GOODWIN PROCESS FOR LINEAR FIRST-ORDER EQUATIONS
77 (p5): 5．APPLICATION OF THE NUMERICAL PROCEDURES
77 (p5-1): 5．1．EQUATIONS WITHOUT EXCHANGE
79 (p5-1-1): 5．1．1．Calculation of Y(γ) and contributions to it
80 (p5-2): 5．2．SOLUTION OF THE RADIAL WAVE EQUATION
81 (p5-2-1): 5．2．1．Starting the outward integrations
82 (p5-2-2): 5．2．2．Starting the inward integrations
84 (p5-3): 5．3．VARIATION EQUATIONS
85 (p5-3-1): 5．3．1．Matching the inward and outward equations
87 (p5-3-2): 5．3．2．Normalization
87 (p5-3-3): 5．3．3．Revision of the estimates of contributions to Z(γ)
88 (p5-4): 5．4．TORRANCE＇S METHOD
90 (p5-5): 5．5．EQUATIONS WITH EXCHANGE
91 (p5-6): 5．6．CALCULATION OF THE Yk FUNCTIONS
93 (p5-7): 5．7．RADIAL WAVE EQUATION WITH EXCHANGE
95 (p5-7-1): 5．7．1．Starting the integrations
96 (p5-8): 5．8．REVISION OF THE ESTIMATES OF THE RADIAL WAVE FUNCTIONS
97 (p5-9): 5．9．OTHER FORMS OF THE RADIAL WAVE EQUATION
101 (p6): 6．CONFIGURATIONS COMPRISING INCOMPLETE GROUPS
101 (p6-1): 6．1．RUSSELL-SAUNDERS COUPLING
103 (p6-2): 6．2．(LS) TERMS FROM A GIVEN CONFIGURATION
106 (p6-3): 6．3．DERIVATION OF THE FORMULA FOR E＇
110 (p6-4): 6．4．STRUCTURE OF THE FORMULA FOR E＇
111 (p6-5): 6．5．EQUATIONS FOR THE RADIAL WAVE FUNCTIONS
113 (p6-6): 6．6．ONE WAVE FUNCTION IN ADDITION TO COMPLETE GROUPS
113 (p6-7): 6．7．DIFFERENT RADIAL WAVE FUNCTIONS WITHIN A SINGLE GROUP
115 (p7): 7．THE VARIATION OF ATOMIC WAVE FUNCTIONS AND FIELDS WITH ATOMIC NUMBER
115 (p7-1): 7．1．THE NEED FOR A PROCEDURE FOR INTERPOLATION WITH RESPECT TO ATOMIC NUMBER
116 (p7-2): 7．2．PURE SCALING
118 (p7-3): 7．3．LIMITING BEHAVIOR OF THE EQUATIONS AND THEIR SOLUTIONS AS N ？
119 (p7-4): 7．4．VARIATION OF THE REDUCED WAVE FUNCTION WITH R FOR FIXED s
123 (p7-4-1): 7．4．1．The (1s) wave function
124 (p7-5): 7．5．VARIATION OF THE SCREENING NUMBERS WITH ATOMIC NUMBER
128 (p7-6): 7．6．FURTHER EXAMINATION OF THE BEHAVIOR OF THE RADIAL WAVE FUNCTIONS AS N ？
132 (p7-7): 7．7．INTERPOLATION OF CONTRIBUTIONS TO Z
134 (p7-8): 7．8．THOMAS-FERMI APPROXIMATION
136 (p8): 8．ENERGY RELATIONS
136 (p8-1): 8．1．THE TOTAL ENERGY AND CONTRIBUTIONS TO IT
137 (p8-2): 8．2．SUBSTITUTION IN THE I INTEGRALS
139 (p8-3): 8．3．ONE INCOMPLETE GROUP
139 (p8-4): 8．4．ENERGY DIFFERENCES BETWEEN THE (LS) TERMS OF A SINGLE INCOMPLETE GROUP
140 (p8-5): 8．5．ONE WAVE FUNCTION IN ADDITION TO COMPLETE GROUPS
145 (p8-6): 8．6．TWO INCOMPLETE GROUPS
146 (p9): 9．RELATIVISTIC EXTENSION
146 (p9-1): 9．1．DIRAC＇S RELATIVISTIC WAVE EQUATION
147 (p9-2): 9．2．FORM OF SOLUTION OF DIRAC＇S EQUATIONS FOR STATIONARY STATES OF AN ELECTRON IN A CENTRAL FIELD
149 (p9-3): 9．3．MANY-ELECTRON ATOM
151 (p9-4): 9．4．SOLUTION OF THE RADIAL WAVE EQUATIONS
153 (p10): 10．BETTER APPROXIMATIONS
153 (p10-1): 10．1．TWO KINDS OF IMPROVEMENTS IN THE APPROXIMATION
155 (p10-2): 10．2．APPROXIMATE WAVE FUNCTIONS INVOLVING γij OR ？ij EXPLICITLY
159 (p10-3): 10．3．SUPERPOSITION OF CONFIGURATIONS
162 (p10-4): 10．4．POLARIZATION
164 (p11): APPENDIX 1．RESULTS OF CALCULATIONS OF ATOMIC STRUCTURES
166 (p12): APPENDIX 2．TABLES OF γ,SCREENING NUMBERS FOR γ,AND REDUCED WAVE FUNCTIONS
174 (p13): APPENDIX 3．ADDENDA
177 (p14): NAME INDEX
179 (p15): SUBJECT INDEX

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2024-06-13