Mathematical Methods for Physicists

The book covers different aspects of mathematical methods for Physics. It is designed for graduate courses but a part of it can also be used by undergraduate students. The leitmotiv of the book is the search for a common mathematical framework for a wide class of apparently disparate physical phenomena. An important role, within this respect, is provided by a nonconventional formulation of special functions and polynomials. The proposed methods simplify the understanding of the relevant technicalities and yield a unifying view to their applications in Physics as well as other branches of science.

The chapters are not organized through the mathematical study of specific problems in Physics, rather they are suggested by the formalism itself. For example, it is shown how the matrix formalism is useful to treat ray Optics, atomic systems evolution, QED, QCD and Feynman diagrams. The methods presented here are simple but rigorous. They allow a fairly substantive tool of analysis for a variety of topics and are useful for beginners as well as the more experienced researchers.

Contents:

• Matrices, Exponential Operators and Physical Applications
• Ordinary and Partial Differential Equations, Evolution Operator Method and Applications
• Hermite Polynomials and Applications
• Laguerre Polynomials, Integral Operators and Applications
• Exercises and Complements I
• Exercises and Complements II
• Exercises and Complements III
• Exercises and Complements IV
• Special Functions, Umbral Methods and Applications
• A Glimpse into the Math of the Feynman Diagrams

Readership: Advanced undergraduate and graduate students in physics and related fields.Matrices;Special Functions and Polynomials;Matrices and Transport Optics;Quantum Mechanics;Schroedinger Equation;Non-Relativistic Quantum Mechanics;Relativity;Relativistic Quantum Mechanics;Angular Momentum and Spin0Key Features:

• The book is formulated with a completely new mathematical language focused on flexibility for treating problems from different branches of physics
• The evolution of symbolic methods has opened new avenues in mathematics and in the relevant applications
• The Authors come from different background (high energy physics, laser and accelerator physics, mathematics) and they have merged the relevant competences to provide a gentle introduction to a modern conception of the use of mathematics in Physics