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Znojil, Miloslav
Reviewer number:
Item's zbl-Number:
DE 015 559 923
Fernandez, Francisco M.
Introduction to perturbation theory in quantum mechanics
Boca Raton, FL: CRC Press, (ISBN 0-8493-1877-7). xii, 271 p. (2001)
81Q15Perturbation theories for operators and differential equations
81-01Instructional exposition textbooks, tutorial papers, etc.
81-02Research exposition monographs, survey articles
81-04Explicit machine computation and programs not the theory of computation or programming
81-08Computational methods
68W30Symbolic computation and algebraic computation
65-04Explicit machine computation and programs not the theory of computation or programming
65B10Summation of series
65Z05Applications to physics
Primary Classification:
Secondary Classification:
Schroedinger equation, Rayleigh-Schroedinger perturbation theory, methods of Dalgarno-Stuart, Fernandez-Castro, Swenson-Danforth, Born-Oppenheimer etc., perturbation theory in classical mechanics

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

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
Rayleigh-Schroedinger 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
field-theoretical 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 many-body
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 large-N 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
Remarks to the editors: