Quantum Mechanics An Introduction To The Physical Background And Mathematical Structure 1st Edition Gregory L Naber by Gregory L. Naber 9783110751611, 9783110751949, 3110751615, 3110751941 instant download after payment.

Preface

The goal here is to provide an introduction to the physical and mathematical foundations of quantum mechanics. It is addressed to those who have been trained in modern mathematics and whose background in physics may not extend much beyond F = mA, but for whom the following sorts of questions require more than a perfunctory response. What are the physical phenomena that forced physicists into such a radical re-evaluation of the very beautiful and quite successful ideas bequeathed to them by the founding fathers of classical physics? Why did this re-evaluation culminate in a view of the world that is probabilistic and formulated in terms of Hilbert spaces and self-adjoint operators? Where did the Planck constant come from? What are the basic assumptions of quantum mechanics? Are they consistent? What motivated them? What objections might be raised to them? Where did the Heisenberg algebra come from? What motivated Feynman to introduce his path integral? Is it really an “integral”? Does it admit a rigorous mathematical definition? Why does one distinguish two “types” of particles in quantum mechanics (bosons and fermions)? Why and how are they treated differently? In what sense does supersymmetry provide a more unified picture of the two types? One need not know the answers to all of these questions in order to study the mathematical formalism of quantum mechanics, but for those who would like to know we will try to provide some answers or, at least, some food for thought. As to the mathematical formalism itself, we will provide careful, detailed and rigorous treatments of just a few of the simplest and most fundamental systems with which quantum mechanics deals in the hope that this will lay the foundation for a deeper study of the physical applications to be found in the literature.

In a sense, the harmonic oscillator is to physics what the set of natural…