Quantum Mechanics For Mathematicians

Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc., as self-adjoint operators in appropriate Hilbert spaces and their spectral analysis. Though a “naïve” treatment exists for dealing with such problems, it is based on finite-dimensional algebra or even infinite-dimensional algebra with bounded operators, resulting in paradoxes and inaccuracies.

The focus of the present work is nonrelativistic and relativistic quantum mechanics with standard applications to the hydrogen atom. The author has aimed at presenting quantum mechanics in a comprehensive yet accessible for mathematicians and other non-physicists. The genesis of quantum mechanics, its applications to basic quantum phenomena, and detailed explanations of the corresponding mathematical methods are presented. The exposition is formalized (whenever possible) on the basis of the coupled Schroedinger, Dirac and Maxwell equations. Aimed at upper graduate and graduate students in mathematical and physical science studies.

Quantization of physical systems requires a correct definition of quantum-mechanical observables, such as the Hamiltonian, momentum, etc., as self-adjoint operators in appropriate Hilbert spaces and their spectral analysis. Though a “naïve” treatment exists for dealing with such problems, it is based on finite-dimensional algebra or even infinite-dimensional algebra with bounded operators, resulting in paradoxes and inaccuracies.

In The Foundations of Quantum Mechanics - Historical Analysis and Open Questions, leading Italian researchers involved in different aspects of the foundations and history of quantum mechanics are brought together in an interdisciplinary debate. The book therefore presents an invaluable overview of the state of Italian work in the field at this moment, and of the open problems that still exist in the foundations of the theory.