Computational Physics FORTRAN:Computational Physics FORTRAN
Preface
Computation is an integral part of modern science and the ability to
exploit effectively the power offered by computers is therefore essential to
a working physicist. The proper application of a computer to modeling
physical systems is far more than blind "number crunching," and the
successful computational physicist draws on a bdanced mix of analytically
soluble examples, physicd intuition, and numerical work to solve problems
that x e otherwige intractable.
Unfortunately, the ability "to computen is seldom cultivated by the
stmdard zrniwrsity-level physics crtrri culum, as it requires an inteaation
of three disciplines (physics, numerical analysis, and computer programming)
covered in disjoint courses. Few physics students finish their undergraduate
education knowing how to compute; those that do usually
leara a L i ~ t e dge t of techniques in the coufse of independent work, such
as a research projed or a senior thesis.
The materid in. this book is ~ m e d r e f i~nge omputationd sEns
in advanced undergraduate ar be@nning graduate students by providixrg
experimce in using a computer to model physical systems. Its s q e
includes the minimam set of numerical techaiques needed to '"do physics"
on a mmputer. Each of these is developed In the text, often hmristicdy,
and is then applied to solve non-trivial problems in classical, qnantum,
and statisticd physics, The= latter have been chosen to enrich or atend
the standard undergraduate physics curriculum, and so haw considerable
intrinsic interest, quite independent of the comput ationd principles they
illustrate,
This book should not be thought of as setting out a rigid or definitive
curriculum. I have restricted its scope to calculations that satisfy
simultaneously the criteria of illustrating a widely applicable numerical
technique, of being tractable on a microcomputer, and of having some
parhicalm physics interest. Several import ant numeric& techniques have
therefore been o ~ t t e ds,p Eae iaterpdatim asld the F a t Fburier Transform
among them. Computational Physics is perhaps best thought of as
establishing m environment rer ring opportunities for further eqloration.
There are =my possible extensions and embelEshmerrts of the materid
prescjnted; using mevs iana&nation dong these liaw is one of the mom
rewwding parts of working through the book.
C"omp.utat%'onaPll tysz'cb? is primwily a physics text, For xnknrum
benefit, the student should have taken, or be taking, undergraduate
courses in dwsical meclzanic~, quantum mechanics, stat;jstical mechmics,
and advanced cafculus m the mathematical methods of physics.
Tbis is slot a text on aurnerical analysis, as there hahs been no attempt at
rigor or completeness in any of the expositions of numerical techniques.
However, a prior course in that subject is probabb not essential; the discussions
of numerical techniques should be accessible to a student with
the physics background outlined above, perhaps with gome reference to
any one of the excellent texts on numerical andysis (for example, [AC~O],
[Bu81], or [Sh84]). This is dso not a text on computer programming. AIthough
I have tried to follow the principles of good programming throughout
(see Appendix B), there has been no attempt to teach programming
per se. Indeed, techniques for organizing and writing code are somewhat
peripheral to the main gods of the book. Some familiarity with programming,
at least to the extent of a one-semester introductory course in any
of the standard high-level languages (BASIC, FORTRAN, PASCAL, C),
is therefore essentid.
The choice of language invariably invokes strong feelings among scientists
who use computers. Any language is, after d, only a mews of
expressing the concqts underlying a program. The contents of this book
are therefore rdevant no m&ter what lanpae;e one vvorfis in. However,
some laneage had to be elrosen to implement the programs, and I have
selected the Microsoft dialect of BASIC standard on the IBM PC/XT/AT
computers for this purpose. The BASIC language has many well-known
deficiencies, foremost among them being a lack of local subroutine variables
and an awkwardness in expressing structured code. Nevertheless, I
believe that these are more than balanced by the simplicity of the language
and the widespread ftuency in it, BASIC'S almost universal avdability
on the microcomputers most likely to be used with this book, the existence
of both BASIC interpreters convenient for writing and debugging
programs and of compilers for producing rapidly executing finished programs,
and the powerful graphics and I/O statements in this language.
I expect that readers familiar with some other high-level language can
learn enough BASIC "on the Ay'' to be able to use this book. A synopsis
of the language is contained in Appendix A to help in this regard, and
further information can be found in readily available manuds. The reader
may, of course, elect to write the programs suggested in the text in any
convenient 1anguag;e.
This book arose out of the Advanced Computational Physics Laboratory
taught to third- and fourth-year undergraduate Physics majors
at Csiltech during the Winter md Spring of 1984, The content ilnd presentation
have benefitted grea;t.ly fram the many inspired suggestims af
M,-C. Chtt, V. PGnisc11, R. WiUiarns, md D. Meredith. Mrs. Mereditb
wads also af great wsistance in producing the find fom of the mannscript
and programs. I. also wish to thank my wife, Laarie, ibr her extraordinary
galienct;, anderstanang, and support during my twa-year involvemeat in
this project.
Contents
Preface, u
Preface Lia the FORTRAN Editiaa, iz
Haw to use this baak, zi
Chapter 1: Basic Mathematical Operations, 1
2 -1 Numerical diEerentiatioa, 2
1.2 Nnnterieal quadratwe, 6
1.3 Finding roots, 11
1.4 Sernidz~ssicdq uantiz-atioa of molecular vibrations, 14
Project I: Scattering by a central potential, &O
Chapter 2: Ordinary DiEerential Equations, 25
2.1 Simple methods, 26
2.2 Multistep and impEcit method@, 89
2.3 Range-Kutta methods, $2
2.4 StabiEdy, $4
2.5 Order and chaos in. two-disniensiand zndion, $7
Project 11: The stmcture of white dwmf stas, 46
11.1 The equations of eqailibrium, 46
11.2 The equation of state, 4 7
11.3 S e d i ~ gth e equations, 50
B.4 Solving the equalians, 51
Chapter 3: Boundary Value and Eigenvalue Prablems, 55
3*1 The Numerov dgorithm, 56
3.2 Direct intepatian of boundav value problems, 57
3.3 Green" function solution of boundary value problems, 61
3.4 Eigenvalues of the wave equ;t;tion, 64
3.5 St ittioaary solutions of the one-dimensional Schroedinger equ*
tion, 67
ziu Contends
Project 111: Atomic structure in the Martree-Fa& approximation, Y23
f 11.1. Basis af the Hartre@F-o ck approximation, 72
IfI,2 The tw-electron problem, 75
112.3 Many-electron systems, 78
If 1.4 S~Ivingth e equations, 80
Chapter 4: Special Functions and Gausshn Quadrature, 85
4.1 Specid funcZlion~, 85
4.2 Gaussian quadrature, 9b
4.3 Born and eiXcond qproSrnadions ta quantum scattering, 96
Project IV: Partial wave solution of quantum scattering, 108
IV.1 Partial wave decomposition of the wave function, 109
IV.2 Finding the phase shifes, 104
IV.3 Sdving the equations, 1135
Chapter 5: Matrix Operations, 109
5.1 M;xtrix inversion, 109
5.2 Eigenvalues of a tri-diagonal matrix, 11 2
5.3 &duction to tri-diagond fom, f L5
5.4 Determining nudear charge densities, Id0
Project V: A schematic shell model, 188
V.1 Definition of the model, 184
KZ The exact dgenstates, 196
V.3 Approximat;e eigenstates, 158
V.4 Solving the model, 149
Chapter 6: Elliptic Partial Differential Equations, 145
6.1 Disercdizatian and the varizttiond principle, 24 7
6.2 An idesstiw method for boundav value problems, 151
6.3 More on, discretizatio~,1 155
6.4 Elliptic equations in two dimensions, 157
Project VI: S teady-state hydrodynamics in two dimensions, 158
VI.l The equations and their diseretization, 159
VI.2 Boundary conditions, f 68
VI.3 Solving the equations, 166
Chapter 7: Pwrabofie Partial DiEerenlial Eqaatiarzs, 169
7.1 Naive discretiz;ztion and instabilities, l69
7.2 Impfici t schemes md the inversion of tri-diagond matrices, 174
"7.3 DiRusion and boundary value problems in tw dimensians, 179
7.4 Iterative methods for eigenvdue problems, 181
7.5 he time-dependent Schroedinger equation, 186
Prdect VXI: Self-osganizaeion in chemical. rextions, 189
V11.1 Descriptiolz of the model, I89
V"11.2 Lillear st abi2ity andysis, 191
VE.3 Nun2erirzd solution of the model, r"$d
Chapter 8: Monte Carto Methods, 197
8.1 The basic Mmte Carlo strategy, 198
8.2 Generating random. variables with a spedfied &&ribation, 205
8.3 The algorithm of Metropolis et al., 210
8.4 The Isiag model in two dimensions, 215
Project VIIZ: Quantum Mm& Cado for the H2 mdecule, 221
VIII.1 S t&ement of the problem, 231
VIII.2 Variational Monte Carlo and the trial wave function, 288
VIII.3 Monte Carlo evaluation of the exact energy, $85
VXII.4 Solving the problem, 229
Appendix A: How to use the programs, 231
AI Insfaflation, 231
A.2 Files, $32
A.3 CompiZatian, 233
A.4 Execution, 635
A5 Graphics, L97
A.6 Prw~amS tructure, $88
A.7 Menu Structure, 259
A.8 Default Value Revision, 241
Appendix B: Programs for the Examples, 849
B,l Example 1, 243
B.2 Exanlplc 2, 256
B.3 Exa~nple 3, $73
B.$ Exampks 4, 295
B.5 Exan113le 5, 316
B.6 Exan3ple G, $89
B.7 Example 7, 370
B.8 Example 8, 991
Appendix C: Programs far the Projects,
C.1 Project I, 409
6.2 Project If, 421
C.3 Project XII, 4914
C.4 Project W, 454
6.5 Project V, $W
C.6 Project, VX, 494
C.7 Project VII, 580
C.8 Project VIfI, @S
Appendix D: Cornman UGilif;y Code@, 567
D.1 Standardization Code, 567
D.2 Hardware and Compiler Specific Code, 570
D.3 General Input/oatpu% Codes, 574
D.4 Graphics Codes, 598
Appendix E: NeLwork Fife =ans&r, 681
Index, 631"
The problem with computers is that they only give answers
-attributed do P. Picasso
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感谢楼主的辛苦工作!:30bb :30bb
感谢楼主分享，正在下载。。。。。。。。。。。。。。。。。
书不错！！！谢谢楼主分享:31bb :31bb
thank you!!!!!!!!
感谢楼主的无私奉献精神！:11bb :30bb
谢谢楼主分享,Fortran在电磁计算中确实很适用:27bb
感谢楼主分享
:11bb :11bb :11bb :11bb
Computational Physics FORTRAN 好书，非常感谢
zhende感谢
感谢楼主的无私奉献精神！
这年头用Fortran的人似乎少了
ganxiefenxiang
正在使用fortran,感谢楼主分享！
nice book, push.{:7_1235:}
计算物理经典，下之
非常感谢lz的分享
多谢分享！
Computational Physics FORTRAN.part01.rar (4.96 MB) 
