The Schrödinger Equation: 66 (Mathematics and its Applications, 66) - Hardcover

Berezin, F.A.; Shubin, M.

Hardcover

ISBN 10: 079231218X ISBN 13: 9780792312185

Publisher: Springer, 1991

Synopsis

4Et moi, ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point alle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non· The series is divergent; therefore we may be sense'. able to do something withit. Eric T. Bell O. Heaviside Mathematicsis a tool for thought. A highly necessary tool in a world whereboth feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ...'; 'One service logic has rendered com­ puter science ...'; 'One service category theory has rendered mathematics ...'. All arguably true. And all statements obtainable this way form part of the raison d'€tre ofthis series.

About this title

Review

' ....interest to both mathematicians and physicists; Highly recommended.' Mathematika 39 1992

Synopsis

This volume deals with those topics of mathematical physics, associated with the study of the Schrodinger equation, which are considered to be the most important. Chapter 1 presents the basic concepts of quantum mechanics. Chapter 2 provides an introduction to the spectral theory of the one-dimensional Schrodinger equation. Chapter 3 opens with a discussion of the spectral theory of the multi-dimensional Schrodinger equation, which is a far more complex case and requires careful consideration of aspects which are trivial in the one-dimensional case. Chapter 4 presents the scattering theory for the multi-dimensional non-relativistic Schrodinger equation, and the final chapter is devoted to quantization and Feynman path integrals. These five main chapters are followed by three supplements, which present material drawn on in the various chapters.The first two supplements deal with general questions concerning the spectral theory of operators in Hilbert space, and necessary information relating to Sobolev spaces and elliptic equations. Supplement 3, which essentially stands alone, introduces the concept of the supermanifold which leads to a more natural treatment of quantization.

Although written primarily for mathematicians who wish to gain a better awareness of the physical aspects of quantum mechanics and related topics, it will also be useful for mathematical physicists who wish to become better acquainted with the mathematical formalism of quantum mechanics.Much of the material included here has been based on lectures given by the authors at Moscow State University, and this volume can also be recommended as a supplementary graduate level introduction to the spectral theory of differential operators with both discrete and continuous spectra. This English edition is a revised, expanded version of the original Soviet publication.

Edition details

• Publisher: Springer
• Publication date: 1991
• Language: English
• ISBN 10: 079231218X
• ISBN 13: 9780792312185
• Binding: Hardcover
• Number of pages: 573