Título: Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators
Autor: Gerald Teschi
Sinopse: 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. It is well suited for self-study and includes numerous exercises (many with hints).
Contexto da obra
Quando a classificação é mais ampla, o contexto do livro costuma depender ainda mais de autoria, tema e edição. “Mathematical Methods in Quantum Mechanics: With Applications to Schrodinger Operators”, de Gerald Teschi, publicado pela editora Amer Mathematical Society, em 2009 e com 305 páginas, integra a categoria Livros Variados. Por isso, autoria, edição e tema acabam tendo ainda mais peso na forma de apresentar o livro.
Editora: Amer Mathematical Society
Páginas: 305
Ano: 2009
Edição: New ed.
Linguagem: pt_BR
ISBN: 9780821846605
ISBN13: 9780821846605
Sobre a editora
Os livros da editora Amer Mathematical Society apresentam uma leitura densa e técnica, voltada para leitores com formação avançada em matemática e áreas correlatas. O catálogo privilegia obras que exploram temas como sistemas dinâmicos, equações diferenciais parciais não lineares e geometria diferencial, com abordagens que combinam rigor teórico e aplicações concretas. A linguagem é predominantemente formal e didática, com exemplos matemáticos detalhados e demonstrações completas, ideal para quem busca aprofundamento acadêmico. Há uma clara ênfase em métodos modernos e clássicos, incluindo tópicos como mecânica hamiltoniana, teoria espectral e análise de sistemas estocásticos.
