Mathematical Methods in Quantum Mechanics
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Home > Mathematics and Science Textbooks > Physics > Quantum physics > Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators(Graduate Studies in Mathematics)
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Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators(Graduate Studies in Mathematics)

Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators(Graduate Studies in Mathematics)


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About the Book

Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrödinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrödinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. This new edition has additions and improvements throughout the book to make the presentation more student friendly.

Table of Contents:
Preface Part 0. Preliminaries Chapter 0. A first look at Banach and Hilbert spaces Part 1. Mathematical foundations of quantum mechanics Chapter 1. Hilbert spaces Chapter 2. Self-adjointness and spectrum Chapter 3. The spectral theorem Chapter 4. Applications of the spectral theorem Chapter 5. Quantum dynamics Chapter 6. Perturbation theory for self-adjoint operators Part 2. Schrödinger operators Chapter 7. The free Schrödinger operator Chapter 8. Algebraic methods Chapter 9. One-dimensional Schrödinger operators Chapter 10. One-particle Schrödinger operators Chapter 11. Atomic Schrödinger operators Chapter 12. Scattering theory Part 3. Appendix Chapter 13. Almost everything about Lebesgue integration Bibliographical notes Bibliography Glossary of notation Index

About the Author :
Gerald Teschl, University of Vienna, Austria.

Review :
The book is written in a very clear and compact style. It is well suited for self-study and includes numerous exercises (many with hints)." - Zentralblatt MATH "The author presents this material in a very clear and detailed way and supplements it by numerous exercises. This makes the book a nice introduction to this exciting field of mathematics." - Mathematical Reviews


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Product Details
  • ISBN-13: 9781470417048
  • Publisher: American Mathematical Society
  • Publisher Imprint: American Mathematical Society
  • Edition: New edition
  • Language: English
  • Series Title: Graduate Studies in Mathematics
  • Weight: 809 gr
  • ISBN-10: 1470417049
  • Publisher Date: 30 Oct 2014
  • Binding: Hardback
  • Height: 229 mm
  • No of Pages: 356
  • Sub Title: With Applications to Schrodinger Operators
  • Width: 152 mm


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Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators(Graduate Studies in Mathematics)
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