[ FreeCourseWeb ] A Miscellany of Mathematical Physics

A Miscellany of Mathematical Physics



English | PDF,EPUB | 2018 | 92 Pages | ISBN : N/A | 2.6 MB

This book is based on eight articles that were written for Resonance. Needless to say, the material has been rearranged, revised, and considerably expanded in some directions, so as to have a degree of cogency. The articles themselves grew out of the notion that the mathematical tools and techniques required by the students of physical sciences can, and should, be introduced to them in a more `user-friendly' style than is generally the case. The initial introduction should be heuristic, with adequate motivation. The development of the subject matter should help the student not only to learn the techniques, but also to gain insight and the ability to recognise interconnections. Attention should be paid to the natural unfolding of the subject matter; one thing should lead to another. While correctness can never be sacrificed, formal rigour and exactitude need not be at the forefront.
In this book, we take a walking tour — or a casual stroll — through a variety of topics, such as vectors, reciprocal vectors, spherical and hyperspherical coordinates, Cartesian tensors, the true meaning of a vector, linear vector spaces, ket and bra vectors, infinitesimal rotation generators, the finite rotation formula, rotation matrices, the orthogonal group and its parameter space, Pauli matrices, the unitary group and its parameter space, the Dirac delta function, Green functions, the wave equation, its Fourier transform, and its fundamental solution in spaces of different dimensions. One thing leads to another!

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