Mathematical Physics by Bergfinnur Durhuus and Jan Philip Solovej

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Mathematical Physics by Bergfinnur Durhuus and Jan Philip Solovej

Mathematical Physics by Bergfinnur Durhuus and Jan Philip Solovej

The main focus of this note is on theoretical
developments rather than elaborating on concrete physical systems, which the
students are supposed to encounter in regular physics courses. Topics covered
includes: Newtonian Mechanics, Lagrangian Mechanics, Hamiltonian Mechanics,
Hilbert Spaces, Operators on Hilbert spaces and Quantum mechanics.

Author(s): Bergfinnur
Durhuus and Jan Philip Solovej

Main goal of this
note is to show the appropriate mathematics to a student of physics, roughly
familiar with all classes of theoretical physics except for quantum field
theory. Topics covered includes: Newtonian mechanics, Lagrangian mechanics,
Classical field theories, Hamiltonian mechanics, Quantum mechanics.

This note describes the following topics: Notation for scalar product, Linear
vector spaces, Operators, Eigenvectors and Eigenvalues, Green’s functions,
Integral Equations, Variational calculus.

This
book is intended primarily as a class-book for mathematical students and
as an introduction to the advanced treatises dealing with the subjects of the
different chapters, but since the analysis is kept as simple as possible, It
will be useful for chemists and others who wish to learn the principles of these
subjects.

This note covers the following topics: Prologue, Free Fall and Harmonic Oscillators, ODEs and SHM, Linear Algebra,
Harmonics - Fourier Series, Function Spaces, Complex Representations, Transform
Techniques, Vector Analysis and EM Waves, Oscillations in Higher Dimensions.