Quantum Theory

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics.

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics.

In addition to traditional topics, this book includes: selective measurements, Wigner's Theorem of symmetry transformations, generators of quantum transformations, supersymmetry, details on the spectra of Hamiltonians and stability of quantum systems, Bose-Fermi oscillators, coherent states, hyperfine structure of the H-atom for any angular momentum, the non-relativistic Lamb shift, anomalous magnetic moment of the electron, Ramsey oscillatory fields methods, measurement, interference and the role of the environment, the AB effect, geometric phases, including non-adiabatic and non-cyclic, Schrödinger's cat and quantum decoherence, quantum teleportation and cryptography, quantum dynamics of the Stern-Gerlach effect, Green functions, path integrals, including constrained dynamics, quantum dynamical principle and variations, systematics of multi-electron atoms, stability of matter, collapse of "bosonic matter" and the role of spin, intricacies of scattering, quantum description of relativistic particles for any spin and mass, spinors, helicity, the Spin and Statistics Theorem. It also contains numerous problems some of which are challenging enough for research.

"Quantum Physics of the Solid State: an Introduction" Draft foreword: 26/09/03 If only this book had been available when I was starting out in science! It would have saved me countless hours of struggle in trying to apply the general ideas of the standard solid-state text-books to solve real problems. The fact is that most of the texts stop at the point where the real difficulties begin.

Bohr and Planck helped shaped the cultural landscape of the world today. Now their work is available here in a digestible, pocket format for the modern reader.