Complex scaling enables one to associate the resonance phenomenon, as it appears in
atomic, molecular, nuclear physics and in chemical reactions, with a single square …

The article surveys the main topics, techniques, and results of the theory of periodic
operators arising in mathematical physics and other areas. Close attention is paid to …

Partial differential equations are a many-faceted subject. Created to describe the
mechanical behavior of objects such as vibrating strings and blowing winds, it has …

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 …

Ever since its invention in 1929 the Dirac equation has played a fundamental role in various
areas of modern physics and mathematics. Its applications are so widespread that a …

This book treats the Atiyah-Singer index theorem using the heat equation, which gives a
local formula for the index of any elliptic complex. Heat equation methods are also used to …

Semiclassical approximation addresses the important relationship between quantum and
classical mechanics. There has been a very strong development in the mathematical theory …

We survey old and recent results dealing with the existence and properties of solutions to
the Choquard type equations-Δ u+ V (x) u=\left (| x|^-(N-α)*| u|^ p\right)| u|^ p-2 u\quad …

The intention of this book is to introduce students to active areas of research in mathematical
physics in a rather direct way minimizing the use of abstract mathematics. The main features …

A theory is the more impressive, the simpler are its premises, the more distinct are the things
it connects, and the broader is its range of applicability. Albert Einstein There are two …