Zentralblatt MATH  REVIEW SUBMISSION FORM 
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Name:  
Znojil, Miloslav  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 015 559 923  
Author(s):  
Fernandez, Francisco M.  
Shorttitle:  
Introduction to perturbation theory in quantum mechanics  
Source:  
Boca Raton, FL: CRC Press, (ISBN 0849318777). xii, 271 p. (2001)  
Classification:  
 
Primary Classification:  
Secondary Classification:  
Keywords:  
Schroedinger equation, RayleighSchroedinger perturbation theory, methods of DalgarnoStuart, FernandezCastro, SwensonDanforth, BornOppenheimer etc., perturbation theory in classical mechanics  
Review:  
Professor Fernandez is active in the field of quantum mechanical perturbation theory for many years. On this and related areas of study and research he has already written several books and cca three hundred papers. Still, this book is a certain very personal climax of his efforts, displaying both his views of the subject and a characteristic style of its presentation at their best. Obviously, the book has been prepared and written with  and to  the author's undisguised delight, offering a specific blend of the theory and computations. In the numerous illustrative examples the emphasis is put on the maximal use of symbolic manipulations before their final and consequent numerical fructification. The student (presumably, the most typical target of the book) is advised to check and reproduce the tables and figures himslef/herself, using the numerous though elementary programs prepared for him/her in MAPLE. On the purely theoretical level, the book complements the standard perturbation chapter of usual textbooks by many fresh views, scattered up to now over scientific journals. The author collects the material and reminds the reader that the current textbook recipes represent really just a very small fraction of all the feasible constructions. Thus, one may enjoy the comparison of the method of Fernandez and Castro with the approach by Swenson and Danforth in chapter five, or check the various technical subtleties when dealing with realistic atomic and molecular models in chapter four. The book informs the reader, in an admirably compact and still unbelievably digestible text, about virtually all the basic concepts (cf. degeneracy and time dependence in chapter one, etc). The eligible strategies of construction are reviewed (cf. chapter two in coordinate representation and chapter three for work without wave functions). All is done, predominantly, from the RayleighSchroedinger point of view. Of course, the very fresh literature is reviewed, with, understandably, main attention (almost 30 percent of references) paid to the author's own production. This underlines the very personal flavor of this monograph's style and, at the same time, indicates also some (if any) of its natural limitations. After all, the major difficulty lies in the limited space needed for the clear and consequent presentation of all the essential details. Still, the omission of some topics can be felt as unnecessary. I would personally appreciate more attention paid to the elementary analyticity features of formulae and/or to their quite important fieldtheoretical context (perhaps, in an extension or continuation of the chapter six about convergence). At the same time, other books must be consulted in the genuine manybody context which has no chance to be included just in a form of a small appendix. We may summarize that the material which was chosen forms a very homogeneous unit, incorporating the scattering (chapter eight) as well as the recently very popular largeN expansions (chapter seven). With a notable exception: The last (ninth) chapter describes the transfer of perturbative ideas to classical mechanics. The positive trace of the author's personality is felt in this courageous inclusion of the less standard topical material.  
Remarks to the editors:  