Mathematics & Mathematical Logic

A computational model is a mathematical structure which is constructed in an easy way and is useful in performing certain computations on the structure. This book discusses how the idea of "computational model" has been formalised by connecting the domain theory with the theory of metric spaces and related topological spaces. The nature of number is also examined, from a synthetic, holistic and interdisciplinary point-of-view, which is mostly mathematical but also encompasses respective psychological, neuro-physiological and philosophical views. Reversible logic circuits are discussed, which are beneficial to both classical and quantum computer design. Three experimental prototypes are used to illustrate how, in the near future, reversible computers will outperform conventional computers, in terms of power dissipation and heat generation. In quantum mechanics and field theory, Schroedinger equation for a single particle in one-dimensional imaginary potential represents one of the most popular schematic non-Hermitian models. Via a solvable square-well approximation technique, this book examines the problems in both the co-ordinate and momentum representations. The optimisation problem is also looked at, which in traditional designs, is stated in precise mathematical terms but in real life, are stated in vague and linguistic terms.