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Loewdin P.-O. Linear algebra for quantum theory
John Wiley & Sons, Inc. , 1998, 470 p. PREFACE :
The subject "Linear Algebra for Quantum Theory" was first given by me as a course called Quantum Chemistry and Solid-State Theory at the 1958 Summer Institute in Valadalen in the Swedish mountains. It was later repeated in more and more extended form at more than 30 Summer Institutes in Scandinavia under the auspices of Uppsala University, Uppsala, Sweden, and at more than 25 Winter Institutes in Florida under the auspices of the University of Florida, Gainesville, Florida.
The development in the 1950s of electronic computers had made it possible for quantum scientists to treat matrices of a very large order, but they also encountered problems they were not accustomed to. I discovered somewhat to my surprise that most of the physics textbooks had little material about similarity transformations and the possibility to bring all matrices to "classical canonical form. " In this regard I started emphasizing the use of sets of projection operators, which were idempotent, mutually exclusive, and formed a resolution of the identity—subjects which at that time were hardly mentioned in any physics textbooks. Since I was personally interested in the combination of quantum theory and the special theory of relativity,
I devoted a great deal of time to the study of linear spaces with an indefinite metric. Part of this material was included in the course, and part was published in regular papers in the standard inteational jouals. Some references are mentioned in the text of this book.
The publication of this book has—for several reasons—been delayed for almost two decades, and it goes without saying that many derivations can today be expressed in a shorter and more elegant form. However, I have been told by many of the previous participants in the Summer and Winter Institutes that they are using the original form of "Linear Algebra for Quantum Theory" in their own teaching, and that—if the book is ever published—they would prefer the original form. Hence, even some errors in the Exercises discovered at an early stage have not been corrected and are left as a challenge to new readers.
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