Erwin Schroedinger

Collected Papers on Wave Mechanics

Description
This third, augmented edition contains the six original, famous papers in which Schrodinger created and developed the subject of Wave Mechanics as published in the original edition. As the author points out, at the time each paper was written the results of the later papers were largely unknown to him. The papers and lectures in this volume were revised by the author and translated into English, and afford the reader a striking and valuable insight into how Wave Mechanics developed.

Contents
Papers
Quantisation as a problem of proper values. Part I
Quantisation as a problem of proper values. Part II
The continuous transition from micro- to macro-mechanics
On the relation between the quantum mechanics of Heisenberg, Born, and Jordan, and that of Schrodinger
Quantisation as a problem of proper values. Part III
Quantisation as a problem of proper values. Part IV
The Compton effect
The energy-momentum theorem for material waves
The exchange of energy according to wave mechanics
Lectures
Derivation of the fundamental idea of wave mechanics from Hamilton's analogy between ordinary mechanics and geometrical optics
Ordinary mechanics only an approximation, which no longer holds for very small systems
Bohr's stationary energy-levels derived as the frequencies of proper vibrations of the waves
Rough description of the wave-systems in the hydrogen atom. Degeneracy. Perturbation
The physical meaning of the wave function. Explanation of the selection rules and of the rules for the polarization of spectral lines
Derivation of the wave equation (properly speaking) which contains the time
An atom as perturbed by an alternating electric field
Theory of secondary radiation and dispersion
Theory of resonance radiation, and of changes of the state of the atom produced by incident radiation whose frequency coincides, or nearly coincides, with a natural emission frequency
Extension of wave mechanics to systems other than a single mass-point
Examples: the oscillator, the rotator
Correction for motion of the nucleus in the hydrogen atom
Perturbation of an arbitrary system
Interaction between two arbitrary systems
The physical meaning of the generalized $\psi$-function

Details:

Publisher: American Mathematical Society
Distributor: American Mathematical Society
Series: AMS Chelsea Publishing
Publication Year: 1982
ISBN: 0-8218-2976-9
Paging: 224 pp.
Binding: Softcover

S Blanchere, D Chafai, P Fougeres, I Gentil, F Malrieu, C Roberto, and G Scheffer

Sur Les Inegalites de Sobolev Logarithmiques

A publication of the Societe Mathematique de France.

Description
This book is an overview of logarithmic Sobolev inequalities. These inequalities have been the subject of intense activity in recent years, from analysis and geometry in finite and infinite dimensions to probability theory and statistical mechanics. And many developments are still to come.

The book is a "pedestrian approach" to logarithmic Sobolev inequalities, accessible to a wide audience. It is divided into several chapters of independent interest. The fundamental example of the Bernoulli and Gaussian distributions is the starting point for logarithmic Sobolev inequalities, as they were defined by Gross in the mid-seventies. Hypercontractivity and tensorisation form two main aspects of these inequalities, which are actually part of the larger family of classical Sobolev inequalities in functional analysis.

A chapter is devoted to the curvature-dimension criterion, which is an efficient tool for establishing functional inequalities. Another chapter describes a characterization of measures which satisfy logarithmic Sobolev or Poincare inequalities on the real line, using Hardy's inequalities.

Interactions with various domains in analysis and probability are developed. A first study deals with the concentration of measure phenomenon, which is useful in statistics as well as geometry. The relationships between logarithmic Sobolev inequalities and the transportation of measures are considered, in particular through their approach to concentration. A control of the speed of convergence to equilibrium of finite state Markov chains is described in terms of the spectral gap and the logarithmic Sobolev constants. The last part is a modern reading of the notion of entropy in information theory and of the several links between information theory and the Euclidean form of the Gaussian logarithmic Sobolev inequality. The genesis of these inequalities can be traced back to the early contributions of Shannon and Stam.

This book focuses on the specific methods and the characteristics of particular topics, rather than the most general fields of study. Chapters are mostly self-contained. The bibliography, without being encyclopedic, tries to give a rather complete state of the art on the topic, including some very recent references.

Contents

Preface
Avant-propos
L'exemple des lois de Bernouilli de Gauss
Sobolev logarithmique et hypercontractivite
Tensorisation et perturbation
Familles d'inegalites fonctionnelles
Le critere de courbure-dimension
Inegalites sur la droite reelle
Concentration de la mesure
Inegalites de Sobolev logarithmique et de transport
Sobolev logarithmique et chaines de Markov finies
Inegalites entropiques en theorie de l'information
Bibliographie
Index

Details:

Publisher: Societe Mathematique de France
Series: Panoramas et Syntheses,Number: 10
Publication Year: 2000
ISBN: 2-85629-105-8
Paging: 213 pp.
Binding: Softcover

Jean-Pierre Serre

Exposes de seminaires
(1950 - 1999)

Series : Documents Mathematiques 1 (2001), viii+259 pages

Resume :
Ce volume regroupe des exposes donnes par J-P. Serre entre 1950 et 1999 dans les seminaires Bourbaki, Cartan, Chevalley et Delange-Pisot-Poitou. Les themes abordes vont de la topologie algebrique a la theorie des nombres en passant par les groupes de Lie, la geometrie algebrique et les formes modulaires. On y trouve a la fois des presentations de travaux d'autres mathematiciens (Borel, Dwork,...) et de travaux plus personnels comme l'expose du seminaire Chevalley sur les espaces fibres algebriques qui devait inspirer a Grothendieck la definition de la cohomologie etale. Aucun de ces textes ne figurait deja dans les quatre volumes des ≪ Collected Papers ≫ de J-P. Serre.

Mots clefs : Groupes localement compacts, groupes de Lie compacts, groupes finis, groupes p-divisibles, cohomologie des groupes, algebres simples, fonctions automorphes, espaces vectoriels topologiques, faisceaux coherents, espaces , homotopie, espaces fibres algebriques, variete d'Albanese, fonction des varietes algebriques, revetements ramifies, exponentielles p-adiques, points rationnels de courbes modulaires

Abstract:
Seminar talks (1950-1999)
This volume gathers seminar talks given by J-P. Serre between 1950 and 1999 in various seminars: Bourbaki, Cartan, Chevalley and Delange-Pisot-Poitou. The themes extend from algebraic topology to number theory, covering also Lie group theory, algebraic geometry and modular forms. It gives a both presentation of works by other mathematicians (Borel, Dwork,...) and personal works, like his talk at the Chevalley seminar on algebraic fibre spaces, which was to inspire Grothendieck for his construction of etale cohomology. None of these texts is available in the four volumes of J-P. Serre's ``Collected Papers''.

Key words: Locally compact groups, compact Lie groups, finite groups, p-divisibles groups, group cohomology, simple algebras, automorphic functions, topological vector spaces, coherent sheaves, spaces, homotopy, algebraic fibre spaces, Albanese varieties, function of algebraic varieties, ramified coverings, p-adiques exponentials, rational points of modular curves

ISBN : 2-85629-103-1

Pierre Colmez - Jean-Pierre Serre (Ed.)

Correspondance Grothendieck-Serre

Series: Documents Mathematiques 2 (2001), xii+288 pages

Resume :
Ce volume contient une grande partie de la correspondance mathematique entre A. Grothendieck et J-P. Serre. Cette correspondance constitue une introduction particulierement vivante a la geometrie algebrique des annees 1955-1965 (periode faste s'il en fut). Le lecteur y decouvrira, en particulier, la genese de certaines des idees de Grothendieck: cohomologie des faisceaux (Tohoku), schemas, Riemann-Roch, groupe fondamental, theoremes d'existence, motifs... Il se fera aussi une idee de l'atmosphere mathematique de cette epoque (Bourbaki, Paris, Harvard, Princeton, guerre d'Algerie,...).

Mots clefs : Cohomologie des faisceaux, schemas, Riemann-Roch, groupe fondamental, theoremes d'existence, motifs

Abstract:
Grothendieck-Serre's correspondence
This volume contains a large part of the mathematical correspondence between A. Grothendieck and J-P. Serre. This correspondence forms a vivid introduction to the algebraic geometry of the years 55-65 (a lucky period, if any). The readers will discover, for instance, the genesis of some of Grothendieck's ideas: Sheaf cohomology (Tohoku), Schemes, Riemann-Roch, Fundamental Group, existence Theorems, Motives... They also will get an idea the mathematical athomsphere of this time (Bourbaki, seminars, Paris, Harvard, Princeton, Algeria war,...).

Key words: Sheaf cohomology, schemes, Riemann-Roch, fundamental group, existence theorems, motives

ISBN : 2-85629-104-X