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Hilbert Space Methods in Quantum Mechanics

2009-01-01 Mathematics
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Release : 2009-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 814/5 ( reviews)

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Book Synopsis Hilbert Space Methods in Quantum Mechanics by : Werner O. Amrein

Download or read book Hilbert Space Methods in Quantum Mechanics written by Werner O. Amrein. This book was released on 2009-01-01. Available in PDF, EPUB and Kindle. Book excerpt: The necessary foundation in quantum mechanics is covered in this book. Topics include basic properties of Hibert spaces, scattering theory, and a number of applications such as the S-matrix, time delay, and the Flux-Across-Surfaces Theorem.

Mathematical Methods in Quantum Mechanics

2009 Mathematics
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Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 604/5 ( reviews)

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Book Synopsis Mathematical Methods in Quantum Mechanics by : Gerald Teschl

Download or read book Mathematical Methods in Quantum Mechanics written by Gerald Teschl. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: 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 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. It is well suited for self-study and includes numerous exercises (many with hints).

Hilbert Space Operators in Quantum Physics

2008-09-24 Science
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Release : 2008-09-24
Genre : Science
Kind : eBook
Book Rating : 701/5 ( reviews)

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Book Synopsis Hilbert Space Operators in Quantum Physics by : Jirí Blank

Download or read book Hilbert Space Operators in Quantum Physics written by Jirí Blank. This book was released on 2008-09-24. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems

1994 Mathematics
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Release : 1994
Genre : Mathematics
Kind : eBook
Book Rating : 532/5 ( reviews)

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Book Synopsis Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems by : Krzysztof Kowalski

Download or read book Methods of Hilbert Spaces in the Theory of Nonlinear Dynamical Systems written by Krzysztof Kowalski. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first monograph on a new powerful method discovered by the author for the study of nonlinear dynamical systems relying on reduction of nonlinear differential equations to the linear abstract Schr”dinger-like equation in Hilbert space. Besides the possibility of unification of many apparently completely different techniques, the ?quantal? Hilbert space formalism introduced enables new original methods to be discovered for solving nonlinear problems arising in investigation of ordinary and partial differential equations as well as difference equations. Applications covered in the book include symmetries and first integrals, linearization transformations, B„cklund transformations, stroboscopic maps, functional equations involving the case of Feigenbaum-Cvitanovic renormalization equations and chaos.

Quantum Computation and Quantum Information

2010-12-09 Science
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Release : 2010-12-09
Genre : Science
Kind : eBook
Book Rating : 488/5 ( reviews)

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Book Synopsis Quantum Computation and Quantum Information by : Michael A. Nielsen

Download or read book Quantum Computation and Quantum Information written by Michael A. Nielsen. This book was released on 2010-12-09. Available in PDF, EPUB and Kindle. Book excerpt: One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.

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