Lectures on the Mathematics of Quantum Mechanics II: Selected TopicsThe first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for selfstudy and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula.

What people are saying  Write a review
Contents
1  
Pseudodifferential Operators Berezin KohnNirenberg BornJordan Quantizations  27 
Compact and Schatten Class Operators Compactness Criteria Bouquet of Inequalities  51 
Periodic Potentials WignerSeitz Cell and Brillouen Zone Bloch and Wannier Functions  82 
Connection with the Properties of a Crystal BornOppenheimer Approximation Edge States and Role of Topology  111 
LieTrotter Formula Wiener Process FeynmanKac Formula  132 
Elements of Probability Theory Construction of Brownian Motion Diffusions  157 
OrnsteinUhlenbeck Process Markov Structure Semigroup Property Paths Over Function Spaces  178 
Scattering Theory TimeDependent Formalism Wave Operators  227 
Time Independent Formalisms FluxAcross Surfaces Enss Method Inverse Scattering  246 
The Method of Enss Propagation Estimates Mourre Method Kato Smoothness Elements of Algebraic Scattering Theory  269 
The NBody Quantum System Spectral Structure and Scattering  293 
Positivity Preserving Maps Markov Semigropus Contractive Dirichlet Forms  315 
Hypercontractivity Logarithmic Sobolev Inequalities Harmonic Group  333 
Measure Gage Spaces Clifford Algebra CAR Relations Fermi Field  351 
373  