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Mathematical methods in quantum mechanics : with applications to Schrodinger operators / Gerald Teschl.

By: Material type: TextTextSeries: Graduate studies in mathematics ; v 157.Publication details: Providence : American Mathematical Society, 2014.Edition: 2nd edDescription: xiv, 358 p. ; 27 cmISBN:
  • 9781470417048 (hbk. : acidfree paper)
Subject(s): DDC classification:
  • 515.724 23 T337
Contents:
0. Preliminaries-- 1. Mathematical foundations of quantum mechanics-- 2. Self-adjointness and spectrum-- 3. The spectral theorem-- 4. Applications of the spectral theorem-- 5. Quantum dynamics-- 6. Perturbation theory for self-adjoint operators-- 7. The free Schrodinger operator-- 8. Algebraic methods-- 9. One-dimensional Schrodinger operators-- 10. One-particle Schrodinger operators-- 11. Atomic Schrodinger operators-- 12. Scattering theory-- Appendix-- Bibliographical notes-- Bibliography-- Glossary of notation-- Index.
Summary: This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger 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 Schrodinger 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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515.724 T337 (Browse shelf(Opens below)) Available 136172
Total holds: 0

Includes bibliographical references (pages 345-348) and index.

0. Preliminaries--
1. Mathematical foundations of quantum mechanics--
2. Self-adjointness and spectrum--
3. The spectral theorem--
4. Applications of the spectral theorem--
5. Quantum dynamics--
6. Perturbation theory for self-adjoint operators--
7. The free Schrodinger operator--
8. Algebraic methods--
9. One-dimensional Schrodinger operators--
10. One-particle Schrodinger operators--
11. Atomic Schrodinger operators--
12. Scattering theory--
Appendix--
Bibliographical notes--
Bibliography--
Glossary of notation--
Index.

This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger 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 Schrodinger 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.

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