Externally indexed torrent

If you are the original uploader, contact staff to have it moved to your account

Textbook in PDF format

This advanced undergraduate and graduate-level text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing questions about the particle, the text gradually leads readers into the development of mathematical techniques that provide the answers. Lebesgue integration theory and complex variables are sometimes involved, but most of the book can be understood without them. Exercises at the end of each chapter provide helpful reinforcement.
Operator Methods in Quantum Mechanics demonstrates the power of operator theory as a tool in the study of quantum mechanics. More specifically, it shows how to use algebraic, representation-independent methods to solve one- and three-dimensional problems, including certain relativistic problems. It explains the applications of commutation relations, shift operators, and the virial, hypervirial, and Hellman-Feyman theorems to the calculation of eigenvalues, matrix elements, and wave functions. Organized into 16 chapters, this book begins by presenting a few simple postulates describing quantum theory and looking at a single particle moving along a straight line. Then, it introduces mathematical techniques that answer questions about the particle. It also discusses the use of spectral theorem in answering various questions concerning observables, along with negative eigenvalues and methods of determining parts of the spectrum or estimating lower bounds. Moreover, it explains the time-independent or stationary-state scattering theory and states, long-range potentials, and completeness and strong completeness. Oscillating potentials, eigenfunction expansions, restricted particles, hard-core potentials, the invariance principle, and the use of trace class operators to treat scattering theory are also described in this book. This volume is a valuable resource for physicists, as well as students of intermediate quantum mechanics and postgraduate students who want to be acquainted with the algebraic method of solving quantum mechanical problems.
Starting with a simple quantum theory postulate, this text introduces mathematical techniques that help answer questions important to physical theory. The entire book is devoted to study of a particle moving in a straight line students develop mathematical techniques by answering questions about the particle.
A Unique and Interesting Book. Yet another "Mathematical Foundations of Quantum Mechanics" - a very unique one!
One-Dimensional Motion
The Spectrum
The Essential Spectrum
The Negative Eigenvalues
Estimating the Spectrum
Scattering Theory
Long-Range Potentials
Time-Independent Theory
Completeness
Strong Completeness
Oscillating Potentials
Eigenfunction Expansions
Restricted Particles
Hard-Core Potentials
The Invariance Principle
Trace Class Operators
Appendicies
Bibliography
Index