Mathematical theory of Feynman path integrals (Lecture notes in mathematics ; 523)

Science & Math

Albeverio, Sergio

Høegh-Krohn, Raphael

Mathematics

Springer

The Bulletin of the American Mathematical Society acclaimed this text as "a welcome addition" to the literature of nonstandard analysis, a field related to number theory, algebra, and topology. The first half presents a complete and self-contained introduction to the subject, and the second part explores applications to stochastic analysis and mathematical physics. The text's opening chapters introduce all of the material needed later, including a nonstandard development of the calculus, aspects of singular perturbation theory related to ordinary differential equations, and applications to topology and functional analysis. A significant portion of the text focuses on applications of nonstandard analysis to probability theory. Starting with nonstandard measure theory, the treatment advances to probability problems that can be represented by hyperfinite nonstandard models. Applications of nonstandard analysis to stochastic processes are treated at length, and the authors present numerous applications to mathematical physics. Additional topics include hyperfinite Dirichlet forms and Markov processes, differential operators, and hyperfinite lattice models.

Nonstandard Methods in Stochastic Analysis and Mathematical Physics (Dover Books on Mathematics)

Fenstad, Jens Erik

Lindstrøm, Tom

Dover Publications

Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.

Solvable Models in Quantum Mechanics (Theoretical and Mathematical Physics)

Gesztesy, Friedrich

Holden, H.

Computers & Technology

Holden, Helge

See the best price to sell, buy, or rent books by Høegh-Krohn, Raphael. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Høegh-Krohn, Raphael