G. Ludwig, University of Marburg, Germany

An Axiomatic Basis for Quantum MechanicsVolume 1

Derivation of HubertSpace Structure1985. 6 figures. X, 243 pages.Hard cover DM 118,-. ISBN 3-540-13773-4

This is a work on the fundamental conceptsof quantum mechanics. Professor Ludwig'saim is to deduce the description of micro-scopic objects solely from a macroscopicdescription of the devices used for theirdetection. The description of a two-partmacrosystem where the microsystem isdiscovered as the system transmitting theinteraction is the main topic of this volume.Empirically founded axioms then give rise tothe Hubert space structure of quantummechanics.

This monograph will not only be animportant source of inspiration for futureresearch but should also appeal to all inter-ested in the fundamental structure of natureand of what we may know about it.

Volume 2

Quantum Mechanicsand Macrosystems1987. 4 figures. IX, 242 pages.Hard cover DM 155,-. ISBN 3-540-17540-7

In the first volume Professor Ludwig basedquantum mechanics on the objective descrip-tion of macroscopic devices. In the secondvolume the method is extended to many ele-mentary systems, leading to the theory of"extrapolated quantum mechanics". Theauthor establishes the statistical mechanics ofmacrosystems, and on this basis he solves theproblem of the measuring process in a con-vincing new way as an interaction betweenmicrosystems and macroscopic devices.

Both volumes together present a consistentdescription of quantum mechanics, themeasuring process and its interpretation.

GϋntherLudwicf

Gϋnther tudwig

volumelDematkm of H&ert Space Stπicture

Springer-VerlagSertift Heidefoepg NewYork Tokyo

Volume 2Ouanttβπ Mscftattics and macfosysteiπs

Sprmger-VertegBerlin Heideϊbepg New York Tokyo

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong KongH e i d e l b e r g e r Platz 3, D-1000 B e r l i n ^ 175 F i f t h Ave., Ne\v York NY 10010, USA 28, Lurke Street,

A 3

Texts and Monographs in PhysicsEditors: W. Beiglbδck, J. L. Birman, R. P. Geroch, E. H. Lieb, T. Regge, W. Thirring

S. A. Albeverio, F. Gesztesy, R. Hβegh-Krohn,H. Holden

Solvable Models inQuantum Mechanics1988. 51 figures. XIV, 452 pages.Hard cover DM 158,-. ISBN 3-540-17841-4

Next to the harmonic oscillator and theCoulomb potential the class of two-bodymodels with point interactions is the only onewhere complete solutions are available. Allmathematical and physical quantities can becalculated explicitly which makes this field ofresearch important also for more complicatedand realistic models in quantum mechanics.The detailed results allow their implementa-tion in numerical codes to analyse propertiesof alloys, impurities, crystal and other fea-tures in solid state quantum physics.

This monograph presents in a systematic waythe mathematical approach and unifies resultsobtained in recent years. The student with asound background in mathematics will get adeeper understanding of Schrδdinger opera-tors and will see many examples which mayeventually be used with profit in courses onquantum mechanics and solid state physics.

The book has textbook potential in mathe-matical physics and is suitable for additionalreading in various fields of theoreticalquantum physics.

Contents: The one-center point interaction. -Point interactions with a finite number ofcenters. - Point interactions with infinitelymany centers. - Appendices. - References.

G. Burner, MPI fur Physik und Astrophyik,Garching, FRG

The Early Universe -Facts and Fiction1988. 180 figures. Approx. 380 pages.Hard cover, in preparation.ISBN 3-540-16187-2

Contents:I. THE STANDARD BIG-BANG COSMO-LOGYThe Cosmological Models. - Facts:Observations of Cosmological Significance. -Thermodynamics of the Early Universe inthe Classical Hot Big Bang Picture. -Can the Standard Model be VerifedExperimentally?II. PARTICLE PHYSICS AND COSMO-LOGYGauge Theories and the Standard Model. -Grand Unification Schemes. - Relic Particlesfrom the Early Universe. - Baryon Synthesis.- The Inflationary Universe.III. DARK MATTER AND GALAXYFORMATIONTypical Scales: From Observations andTheory. - The Evolution of Small Pertur-bations. - Computer Simulations and theLarge-Scale Structure.

A. Bohm

Quantum Mechanics:Foundations and Applications2nd edition 1986. 94 figures. XVII, 596 pages.Hard cover DM 135,-. ISBN 3-540-13985-0

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A 4

Texts and Monographs in PhysicsEditors: W. Beiglbδck, J. L. Birman, R. P. Geroch, E. H. Lieb, T. Regge, W. Thirring

O. Bratteli, D. W. Robinson

Operator Algebras and QuantumStatistical Mechanics I

C*- and W*-Algebras, Symmetry Groups,Decomposition of States

2nd edition 1987. XIV, 505 pages.Hard cover DM 134,-. ISBN 3-540-17093-6

Operator Algebras and QuantumStatistical Mechanics IIEquilibrium States. Models in QuantumStatistical Mechanics

1981. XI, 505 pages.Hard cover DM 102,-. ISBN 3-540-10381-3

"...I strongly recommend this book to anyonewishing to understand the foundations ofquantum statistical mechanics. The authorssucceed in convincing you about the natural-ness and utility of algebraic methods."

Revue Roumaine de Physique

Here is the first really thorough andconsistently developed presentation in twovolumes of the applications of operatoralgebra theory to statistical physics.

The authors choose an approach which isparticularly useful from the physicist's pointof view, and all proofs are worked out indetail, making the book an excellent advanc-ed text in mathematics and the first textbookin the field.

K. Chadan, P. C. Sabatier

Inverse Problemsin Quantum Scattering Theory2nd revised and enlarged edition 1988.Hard cover, in preparation.ISBN 3-540-18731-6

From the reviews of the first edition:"There are many books on quantummechanics which show how to calculate thescattering phase shifts from a given potentialbut there has been a lack of a book describingthe extensive literature on the inverseproblem of deriving the potential from thephysical scattering amplitude. This has beenvery adequately filled by the present volumewhich should be read by any serious studentof potential scattering." n, n „p & Physics Bulletin

M. Chaichan, N. F. Nelipa

Introduction toGauge Field Theories1984. 75 figures. XII, 332 pages.Hard cover DM 130,-. ISBN 3-540-13008-X

G. Gallavotti

The Elements of Mechanics1983. 53 figures. XIV, 575 pages.Hard cover DM 118,-. ISBN 3-540-11753-9

This is a detailed introduction to the tech-niques and problems of classical mechanics.

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A 5

Texts and Monographs in PhysicsEditors: W. Beiglbock, J. L. Birman, R. P. Geroch, E. H. Lieb, T. Regge, W. Thirring

H. L. Cycon, R. G. Froese, W. Kitsch,B. Simon

Schrδdinger Operatorswith Applications to Quantum Mechanics andGlobal Geometry

1987. 2 figures. IX, 319 pages.Soft cover DM 56,-. ISBN 3-540-16758-7

A complete understanding of Schrodingeroperators is a necessary prerequisite forunveiling the physics of nonrelativisticquantum mechanics. Recent research showsthat it also helps to deepen our insight intoglobal differential geometry. This monograph,written for both graduate students and re-searchers, summarizes and synthesizes thetheory of Schrodinger operators, emphasizingthe progress made in the last decade by Lieb,Enss, Witten and others. Besides generalproperties, the book covers multiparticlequantum mechanics, including bound statesof Coulomb systems and scattering theory,quantum mechanics in constant electric andmagnetic fields, Schrδdinger operators withrandom and almost periodic potentials, andSchrodinger operator methods in differentialgeometry to prove the Morse inequalities andthe index theorem.

Contents: Self-Adjointness. - LΛProperties ofEigenfunctions, and All That. - GeometricMethods for Bound States. - Local Commu-tator Estimates. - Phase Space Analysis ofScattering. - Magnetic Fields. - ElectricFields. - Complex Scaling. - Random JacobiMatrices. - Almost Periodic Jacobi Matrices.- Witten's Proof of the Morse Inequalities. -Patodi's Proof of the Gauss-Bonnet-ChernTheorem and Superproofs of Index Theo-rems. - Bibliography. - List of Symbols. -Subject Index.

W. Greiner, B. Mϋller, J. Rafelski

Quantum Electrodynamicsof Strong FieldsWith an Introduction into ModernRelativistic Quantum Mechanics

1985. 258 figures. XI, 594 pages.Hard cover DM 140,-. ISBN 3-540-13404-2

R. G. Newton

Scattering Theory of Wavesand Particles2nd edition 1982. 35 figures. XX, 743 pages.Hard cover DM 130,-. ISBN 3-540-10950-1

"Clearly this treatise is an excellent textbook,the best existing one on the subject."

Mathematical Reviews

J. M. Jauch, F. Rohrlich

The Theory of Photonsand ElectronsThe Relativistic Quantum Field Theoryof Charge Particles with Spin One-half

2nd corrected printing of the 2nd expandededition 1980. 64 figures, 10 tables.XIX, 533 pages.Hard cover DM 88,-. ISBN 3-540-07295-0

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A 6

Texts and Monographs in PhysicsEditors: W. Beiglbδck, J. L. Birman, R. P. Geroch, E. H. Lieb, T. Regge, W. Thirring

G. Ludwig

Foundations of QuantumMechanics ITranslated by C. A. Hein

1983. XII, 426 pages.Hard cover DM 140,-. ISBN 3-540-11683-4

Foundations of QuantumMechanics IITranslated by C. A. Hein

1985. 54 figures. XVI, 416 pages.Hard cover DM 228,-. ISBN 3-540-13009-8

For more than three decades GiintherLudwig has made brilliant contributions tothe foundations of quantum physics. This isthe first textbook, in two volumes, thatpresents his theory. Mathematically thoroughand rigorous, these volumes documentimportant progress towards the axiomaticformulation of quantum theory.

In Volume I the author presents the funda-mental concepts of quantum mechanics fromfirst principles. In particular his concept of"effect" becomes the important link betweenexperiment and theory. In Volume II heshows how the basic concepts can be appliedto problems of atomic spectra, structure andspectra of molecules, and scattering theory.

A. Perelomov

Generalized Coherent Statesand Their Applications1986. XI, 320 pages.Hard cover DM 134,-. ISBN 3-540-15912-6

R. D. Richtmyer

Principles of AdvancedMathematical Physics

Volume 1

1978. 45 figures. XV, 422 pages.Hard cover DM 86,-. ISBN 3-540-08873-3

Volume 2

1981. 60 figures. XI, 322 pages.Hard cover DM 88,-. ISBN 3-540-10772-X

N. Straumann

General Relativityand Relativistic Astrophysics1984. 81 figures. XIII, 459 pages.Hard cover DM 112,-. ISBN 3-540-13010-1

F. J. Yndurian

Quantum ChromodynamicsAn Introduction to the Theory of Quarksand Gluons

1983. 31 figures. XI, 227 pages.Hard cover DM 96,-. ISBN 3-540-13752-0

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A 7

Springer Series in SynergeticsEditor: H. Haken

Volume 13

C. W. Gardiner

Handbook of StochasticMethodsfor Physics, Chemistry and the NaturalSciences

2nd edition 1985. 29 figures. XIX, 442 pages.Soft cover DM 99,-. ISBN 3-540-15607-0

Volume 37

W. Gϋttinger, G. Dangelmayr (Editors)

The Physics ofStructure FormationTheory and Simulation

Proceedings of the International Symposium,Tubingen, FRG, October 27 - November 2,1986

1987. 207 figures. XIII, 427 pages.Hard cover DM 109,-. ISBN 3-540-18383-3

The Physics of Structure Formation presentsreports by distinguished authors on recentadvances in our understanding of the mecha-nisms by which patterns are generated innature. Nonlinear dynamics, instabilities andbifurcations through which patterns evolveplay a major role. The topics include structureformation and pattern recognition in dis-ordered systems and in neural networks,interfacial patterns, diffusion limited aggre-gation, the growth of fractal structures, con-vection patterns in fluids, chaotic dynamicsand turbulence.

Volume 18

H. Risken

The Fokker-Planck EquationMethods of Solution and Applications

New edition in preparation

The Fokker-Planck equation deals with thosefluctuations of systems which stem frommany tiny disturbances, each of whichchanges the variables of the system in anunpredictable way. This boqk deals with thederivation of the equation and the methodsfor solving it. The methods are applied to thestatistics of a simple laser model and toBrownian motion in potentials.

Volume 38

H. Haken (Editor)

Computational Systems -Natural and ArtificialProceedings of the International Symposiumon SynergeticsSchloss Elmau, Bavaria, FRG, May 4-9, 1987

1987. 115 figures. VIII, 215 pages.Hard cover DM 90,-. ISBN 3-540-18477-5

The aim of this interdisciplinary book is topresent the most recent results of leadingscientists in neurobiology, computers andphysics. Special emphasis is placed upondrawing a coherent picture of the variousefforts and of our present understanding ofpattern recognition and associative memory.

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A 8

Springer Series in SynergeticsEditor: H. Haken

Volume 20

H. Haken, University of Stuttgart, FRG

Advanced SynergeticsInstability Hierarchies of Self-OrganizingSystems and Devices

1983. Corrected printing 1987.105 figures. XV, 356 pages.Hard cover DM 98,-. ISBN 3-540-12162-5

Systems in diverse disciplines can show simi-lar behavior. When external conditions arechanged, the individual parts of these systemscan organize themselves into new macro-scopic states at certain instability points. Theinstabilities can form hierarchies leading tomore and more complicated patterns of struc-ture and behavior.

This book is a thorough presentation ofrecently developed methods to cope withsuch instability hierarchies. The introductorychapter presents numerous examples fromphysics, electrical engineering, mechanicalengineering, chemistry, biology, economicsand other fields. The approach is based onthe concepts of instability, the slaving prin-ciple, and order parameters. A thorough treat-ment of linear differential equations includingthose with quasiperiodic coefficients and anoutline of the Ito and Stratonovich approachto nonlinear stochastic differential equationsis given. For such equations, the slaving prin-ciple, which allows an enormous reduction ofthe degrees of freedom at instability points, isderived. The resulting order parameter equa-tions, which in the absence of fluctuationsdescribe various kinds of bifurcations of fixedpoints, limit cycles (Hopf bifurcation), toriand chaotic attractors, are presented in detailand the corresponding solutions are derived.

Volume 40

H. Haken, University of Stuttgart, FRG

Information and Self-OrganizationA Macroscopic Approach to Complex Systems

8. 58 figures. XII, 196 pages.Hard cover DM 98,-. ISBN 3-540-18639-5

Complex systems are ubiquitous and practi-cally all branches of science, ranging fromphysics through chemistry and biology toeconomy and sociology, have to deal withthem. This book presents the concepts andmethods needed to deal with complexsystems from a unifying point of view whosebasic idea stems from synergetics. Attentionis focused on those situations where acomplex system changes its macroscopicspatial, temporal or functional structure quali-tatively without specific interference fromoutside, i. e. by self-organization. Whilesynergetics starts from the microscopic level,this book presents an approach that usesmacroscopic data. The vehicle used isinformation. Since this word can have quitedifferent meanings, its various aspects arediscussed. These range from Shannon infor-mation and the effects of information onreceivers to the self-creation of meaning. Thebook utilizes the general formulation ofJaynes' maximum information entropy prin-ciple. With the aid of results from synergetics,adequate objective constraints for a large classof self-organizing systems which form a newstructure via a "nonequilibrium phase transi-tion" are presented. Thus the approachapplies to situations which are among themost interesting ones.

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A 9

James GlimmArthur Jaffe

SecondMtion

A Functional IntegralPoint of View

J. Glimm, Courant Institute for MathematicalSciences, New York University, NY;A. Jaffe, Harvard University, Cambridge, MA,USA

Quantum PhysicsA Functional Integral Point of View

2nd edition 1987. 51 figures. XXII, 535 pages.Hard cover DM 112,-. ISBN 3-540-96476-2Soft cover DM 56,-. ISBN 3-540-96477-0

Quantum Physics develops the mathematicalstructure of quantum theory and statisticalmechanics. The central theme of the book isthe quantization of nonlinear fields.The second edition includes new chapters oncorrelation inequalities and the clusterexpansion, as well as one on the physical andmathematical requirements of nonabeliangauge theories.

From the reviews of the first edition:

"Quantum Physics provides a view ofconstructive quantum field theory, andrelated fields in statistical mechanics, by thetwo researchers with the greatest insights intothe theory...The presentation has many pleasantsurprises." ,, . . , n .

- Mathematical Reviews

"... an important contribution towardestablishing communication between the twocommunities [mathematics and physics]. Theconnection between quantum field theoryand statistical mechanics is made early andused extensively throughout. The expositionis exceptionally crisp and clear. Theoreticalphysicists interested in learning the subjectstreated need look no further."

- Physics Today

"This book is a milestone in the theory ofquantized fields The impact of this bookon mathematics will be profound . . . It is anastounding achievement to have developedthe theory given in this book."

- Bulletin of the London Mathematical Society

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A 10

Springer Series in Solid-State SciencesEditors: M. Cardona, P. Fulde, K. von Klitzing, H.-J. Queisser

Volume 64

W. Ludwig, C. Falter

Symmetries in PhysicsGroup Theory Applied to Physical Problems

1988. 87 figures. XI, 461 pages.Hard cover DM 98,-. ISBN 3-540-18021-4

We all know that symmetry is fundamentallyimportant in physics. On one hand, the sym-metry of a system is often the starting pointfor general physical considerations, and onthe other hand, particular problems may besolved in simpler and more elegant ways ifsymmetry is taken into account.

This book presents the underlying theories ofsymmetry and gives examples of their applica-tion in branches of physics ranging fromsolid-state to high-energy physics via atomicand molecular physics. Finite discretesymmetries, continuous symmetries and alsosymmetry breaking are discussed, andexercises are provided which are intended tostimulate the reader to carry out originalwork.

Volume 19

G. Eilenberger

SolitonsMathematical Methods for Physicists

2nd corrected printing 1983. 31 figures.VIII, 192 pages.Soft cover DM 64,-. ISBN 3-540-10223-X

"This impressive book - with its exhaustivebibliography of over 500 articles - will serveequally well as an advanced text and anauthoritative reference guide to the mathe-matics of solitons. It is ideally suited forengineers, physicists and applied mathemati-cιans •" Physics Today

Volume 20

M. Toda

Theory of Nonlinear Lattices2nd edition 1988. 40 figures.Approx. 240 pages.Soft cover DM 60,-ISBN 3-540-18327-2

Soliton theory, the theory of nonlinear wavesin lattices composed of particles interactingby nonlinear forces, is treated rigorously inthis book. The presentation is coherent andself-contained, starting with pioneering workand extending to the most recent advances inthe field. Special attention is focused on exactmethods of solution of nonlinear problemsand on the exact mathematical treatment ofnonlinear lattice vibrations. This new editionupdates the material to take account ofimportant new advances.

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A l l

Graduate Texts in Contemporary PhysicsEditors: J. L. Birman, H. Faissner

This new series is intended to introducegraduate students to the latest developmentsin physics. The aim is to give them the meansto take an active part in further research inthese developing areas.

In preparation:

H. V. Klapdor (Editor)

NeutrinosWith contributions by F. T. Avignone,R. L. Brodzinski, P. Depommier,F. von Feilitzsch, G. Gelmini,W. Hillenbrandt, H. V. Klapdor,P. Langacker, S. P. Mikheyev,R. N. Mohapatra, K. Muto, A. Y. Smirnow,K. Winter1988. 164 figures. Approx. 350 pages.Hard cover. ISBN 3-540-50166-5

Rabindra N. Mohapatra,University of Maryland, College Park

Unification and SupersymmetryThe Frontiers of Quark-Lepton Physics

1986. 49 figures. XIII, 309 pages.Hard cover DM 92,-. ISBN 3-540-96285-9

Unification and Supersymmetry is a pedago-gical introduction to the techniques of super-symmetric field theories and covers topicssuch as the implications of physical Gold-stone bosons, strong CP-violation, baryonnon-conservation, and left-right symmetry,among others. In addition, it provides a com-prehensive list of references to relevant worksfor the benefit of advanced graduate studentsin elementary particle theory, as well as topostdoctoral particle theorists and experimen-talists.Contents: Important Basic Concepts inParticle Physics. - Spontaneous SymmetryBreaking, Nambu-Goldstone Bosons, and theHiggs Mechanism. - The SU(2)L x U(l)Model. - CP-Violation: Weak and Strong. -Grand Unification and the SU(5) Model. -Left-Right Symmetric Models of WeakInteractions. - SO(10) Grand Unification. -Technicolor and Compositeness. - GlobalSupersymmetry. - Field Theories with GlobalSupersymmetry. - Broken Supersymmetryand Application to Particle Physics. -Phenomenology of Supersymmetric Models.- Supersymmetric Grand Unification. - LocalSupersymmetry (N = 1). - Application ofSupergravity (N = 1) to Particle Physics. -Beyond N = 1 Supergravity.

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A 12

Graduate Texts in Contemporary PhysicsEditors: J. L. Birman, H. Faissner

Richard E. Prange, Steven M. Girvin (Editors)

The Quantum Hall Effect1987. 116 figures. XVII, 419 pages.Hard cover DM 68,-. ISBN 3-540-96286-7

This is the first full-scale overview of thequantum Hall effect, an intriguing fundamen-tal discovery in solid-state physics with appli-cations to semiconductor devices, elementaryparticle theory, and electrical metrology.

The Foreword was written by Klaus vonKlitzing, who was awarded the 1985 NobelPrize in Physics for his discovery of thequantum Hall effect.

Jeffrey W. Lynn, University of Maryland,College Park (Editor)

High-TemperatureSuperconductivity1988. Approx. 350 pages.Hard cover, in preparation.ISBN 3-540-96770-2

This book provides a unified, graduate-leveltutorial on the latest breakthroughs in thetheory and applications of high-temperaturesuperconductivity, from courses given at theUniversity of Maryland, College Park.

Michio Kaku, CUNY, New York, USA

Introduction to Superstrings1988. 48 figures. XVI, 568 pages.Hard cover DM 98,-. ISBN 3-540-96700-1

This comprehensive tutorial introduces thedevelopment of, and current trends in, super-string theory, a significant and still contro-versial attempt to unify general relativity andquantum field theory. Intended for graduatestudents with a year of quantum mechanicsand familiarity with relativistic methods, thebook makes these exciting developmentsavailable to physicists, mathematicians, andothers for the first time in one volume.

Stressing current areas of research activity,Introduction to Superstrings addresses allrelevant topics including string field theory,multi-loops and Teichmuller spaces, confor-mal field theory, and four-dimensional super-strings. Professor Kaku is currently leadingseminars in superspring theory at the Gra-duate Center of the City University of NewYork.

Contents:I. FIRST QUANTIZATION AND PATHINTEGRALS: Path Integrals and PointParticles. Nambu-Goto Strings. Superstrings.Conformal Field Theory and Kac-MoodyAlgebras. Multi-Loops and TeichmullerSpace.II. SECOND QUANTIZATION AND THESEARCH FOR GEOMETRY: Light ConeField Theory. BRST Field Theory. GeometricString Field Theory.III. MODEL BUILDING ANDPHENOMENOLOGY: Anomalies and theAtiyah-Singer Theorem. Heterotic Stringsand Compactification. Calabi-Yau Spaces andOrbifolds.- References. - Appendix.

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A 13

E. W. Schmid, G. Spitz, W. Losch

Theoretical Physicson thePersonal ComputerTranslated from the German edition of 1987

1988. 152 figures. XI, 211 pages.Hard cover DM 79,-. ISBN 3-540-18908-4

Theoretical Physics on the Personal Computeris a novel, easy-to-comprehend and well-structured text, ideal as an introduction toproblem-solving with computers for advancedundergraduate students.

Sixteen instructive chapters are included inthis book, covering the fields of classicalmechanics, wave physics, electrodynamics,thermodynamics and quantum mechanics. Ineach chapter, a problem is first explained andplaced into its physical context before an out-line of the appropriate numerical steps, thecorresponding program in FORTRAN 77 andvarious related problems are discussed. Thefinal section of each chapter discusses thesolutions and gives examples of graphicsoutputs.

The required software for this book isincluded on floppy disk. It has been designedfor the IBM PC/AT and can be used oncompatibles and mainframes with only minorchanges.

For students and lecturers this book willprove to be an indispensable guide for classesin physics, applied mathematics, computerscience and engineering.

Contents: Introduction. - Numerical Differen-tiation and Introduction into Screen Dia-logue. - Numerical Integration. - HarmonicOscillations with Sliding and Static Friction. -

Anharmonic Free and Forced Oscillations. -Coupled Harmonic Oscillations. - The FlightPath of a Space Craft as a Solution of theHAMILTON Equations. - The CelestialMechanics Three-body Problem. - Compu-tation of Electric Fields by the Method ofSuccessive Overrelaxation. - The VAN DERWAALS Equation. - Solution of theFOURIER Heat Conduction Equation andthe "Geo-power Station". - Group and PhaseVelocity in the Example of Water Waves. -Solution of the Radial SCHRODINGEREquation by the FOX-GOODWIN Method. -The Quantum Mechanical Harmonic Oscilla-tor. - Solution of the SCHRODINGEREquation in Harmonic Oscillator Represen-tation. - The Ground State of the HeliumAtom by the HYLLERAAS Method. -The Spherical Harmonics. - The SphericalBESSEL Functions. - Scattering of anUncharged Particle from a SphericallySymmetric Potential. - Appendix.

E.W Schmid G. Spitz WLδsch

Theoreticalon the

Personal

Springer-Verlag

Springer-VerlagBerlin Heidelberg New York London Paris Tokyo Hong Kong

A 14

Optimal ControlF. Colonius

Optimal Periodic Control1988. VI, 177 pages. (Lecture Notes in Mathematics, Volume 1313).Soft cover DM 28,50. ISBN 3-540-19249-2

Contents: Introduction. - Optimization Theory. - Retarded Functional Differen-tial Equations. - Strong Local Minima. - Weak Local Minima. - Local RelaxedMinima. - Tests for Local Properness. - A Scenario for Local Properness. - Opti-mal Periodic Control of Ordinary Differential Equations. - References.

This research monograph deals with optimal periodic control problems forsystems governed by ordinary and functional differential equations of retardedtype. Particular attention is given to the problem of local properness, i.e. whethersystem performance can be improved by introducing periodic motions.Using either Ekeland's Variational Principle or optimization theory in Banachspaces, necessary optimality conditions are proved. In particular, complete proofsof second-order conditions are included and the result is used for various versionsof the optimal periodic control problem. Furthermore a scenario for local proper-ness (related to Hopf bifurcation) is drawn up, giving hints as to where to look foroptimal periodic solutions. The book provides mathematically rigorous proofs forresults which are potentially of importance in chemical engineering and aerospaceengineering.

Springer-Verlag BerlinHeidelberg New York LondonParis Tokyo Hong KongHeidelberger Platz 3, D-1000 Berlin 33 175 Fifth Ave ,New York, NY 10010, USA 28, Lurke Street, BedfordMK40 3HU, England 26, rue des Carmes, F-75005 Pan37-3, Hongo 3-chome, Bunkyo-ku, Tokyo 113, JapanCiticorp Centre, Room 1603, 18 Whitfield Road,Causeway Bay, Hong Kong

In preparation c

C.K Chui, G.Chen 1

Linear Systems andOptimal Control1988. 4 figures. Approx. 120 pages. (Springer Series in Information Sciences,Volume 18). Hard cover DM 98,-. ISBN 3-540-18737-5

Contents: State-Space Descriptions. - State Transition Equations and Matrixes. -Controllability. - Observability and Dual Systems. - Time-Invariant LinearSystems. - Stability. - Optimal Control Problems and Variational Methods. -Dynamic Programming. - The Minimum-Time Optimal Control Problems. -Notes and References. - References. - Answers and Hints to Exercises. - Nota-tion. - Subject Index.

This book offers a self-contained, elementary and yet rigorous treatment of linearsystem theory and optimal control theory. Fundamental topics within this areaare considered, first in the continuous-time and then in the discrete-time setting.Both time-varying and time-invariant cases are investigated. The approach is quitestandard but a number of new results are also included, as are some brief applica-tions. It provides a firm basis for further study and should be useful to all thoseinterested in the rapidly developing subjects of systems engineering, optimalcontrol theory and signal processing.

A 15

Communications in

MathematicalPhysics

Chief Editor A. Jaffe, Cambridge, MA

Editorial Board

Advisory Board

M. Aizenman, New York, NYL. Alvarez-Gaume, GeneveH.Araki, KyotoA. Connes, Bures-sur-YvetteJ.-P. Eckmann, GeneveM. E. Fisher, College Park, IN/IDJ.Frόhlich, ZurichK. Gawedzki, Bures-sur-YvetteJ. L. Lebowitz, New Brunswick, NJJ.Mather, Princeton, NJG. Parisi, RomaB. Simon, Pasadena, CA

Ύa. G. Sinai, MoscowT. Spencer, Princeton, NJS.-T. Yau, Cambridge, MA

M.F.Atiyah, OxfordF. Hirzebruch, BonnG.'tHooft, UtrechtR.Schrieffer, Santa Barbara, CAI. Singer, Cambridge, MAC. N. Yang, Stony Brook, NY

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