Mathematical Methods In Quantum Mechanics: With Applications To Schrodinger Operators (graduate Studies In Mathematics)
by Gerald Teschl /
2014 / English / DjVu
4.8 MB Download
Quantum mechanics and the theory of operators on Hilbert space have
been deeply linked since their beginnings in the early twentieth
century. States of a quantum system correspond to certain elements
of the configuration space and observables correspond to certain
operators on the space. This book is a brief, but self-contained,
introduction to the mathematical methods of quantum mechanics, with
a view towards applications to Schrodinger operators. Part 1 of the
book is a concise introduction to the spectral theory of unbounded
operators. Only those topics that will be needed for later
applications are covered. The spectral theorem is a central topic
in this approach and is introduced at an early stage. Part 2 starts
with the free Schrodinger equation and computes the free resolvent
and time evolution. Position, momentum, and angular momentum are
discussed via algebraic methods. Various mathematical methods are
developed, which are then used to compute the spectrum of the
hydrogen atom. Further topics include the nondegeneracy of the
ground state, spectra of atoms, and scattering theory. This book
serves as a self-contained introduction to spectral theory of
unbounded operators in Hilbert space with full proofs and minimal
prerequisites: Only a solid knowledge of advanced calculus and a
one-semester introduction to complex analysis are required. In
particular, no functional analysis and no Lebesgue integration
theory are assumed. It develops the mathematical tools necessary to
prove some key results in nonrelativistic quantum mechanics.
Mathematical Methods in Quantum Mechanics is intended for beginning
graduate students in both mathematics and physics and provides a
solid foundation for reading more advanced books and current
research literature. This new edition has additions and
improvements throughout the book to make the presentation more
student friendly.
Quantum mechanics and the theory of operators on Hilbert space have
been deeply linked since their beginnings in the early twentieth
century. States of a quantum system correspond to certain elements
of the configuration space and observables correspond to certain
operators on the space. This book is a brief, but self-contained,
introduction to the mathematical methods of quantum mechanics, with
a view towards applications to Schrodinger operators. Part 1 of the
book is a concise introduction to the spectral theory of unbounded
operators. Only those topics that will be needed for later
applications are covered. The spectral theorem is a central topic
in this approach and is introduced at an early stage. Part 2 starts
with the free Schrodinger equation and computes the free resolvent
and time evolution. Position, momentum, and angular momentum are
discussed via algebraic methods. Various mathematical methods are
developed, which are then used to compute the spectrum of the
hydrogen atom. Further topics include the nondegeneracy of the
ground state, spectra of atoms, and scattering theory. This book
serves as a self-contained introduction to spectral theory of
unbounded operators in Hilbert space with full proofs and minimal
prerequisites: Only a solid knowledge of advanced calculus and a
one-semester introduction to complex analysis are required. In
particular, no functional analysis and no Lebesgue integration
theory are assumed. It develops the mathematical tools necessary to
prove some key results in nonrelativistic quantum mechanics.
Mathematical Methods in Quantum Mechanics is intended for beginning
graduate students in both mathematics and physics and provides a
solid foundation for reading more advanced books and current
research literature. This new edition has additions and
improvements throughout the book to make the presentation more
student friendly.
