This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrodinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical...
This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical...
Vladimir Georgiev Alessandro Michelangeli Raffaele Scandone
This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schrödinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are...
This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant l...
This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann and Krein–Vishik–Birman extension schemes both in their modern form and from a historical perspective, and provides a detailed analysis of a range of applications beyond the standard pedagogical examples (the latter are indexed in a final appendix for the reader’s convenience).Self-adjointness of operators on Hilbert space representing quantum observables, in particular quantum Hamiltonians, is required to ensure real-valued energy levels,...
This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann ...
This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vectorfin a Hilbert spaceH, a linear operatorAacting onH, and a vectorginHsatisfyingAf=g, one is interested in approximatingfby finite linear combinations ofg,Ag,A2g,A3g, … The closed subspace generated by the latter vectors is called the Krylov subspace ofHgenerated bygandA. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text.After giving a broad introduction to the subject, examples...
This book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vectorfin a Hilbert spac...
