Basic Theoretical Physics

This concise treatment embraces, in four parts, all the main aspects of theoretical physics (I . Mechanics and Basic Relativity, II. Electrodynamics and Aspects of Optics, III. Non-relativistic Quantum Mechanics, IV. Thermodynamics and Statistical Physics). It summarizes the material that every graduate student, physicist working in industry, or physics teacher should master during his or her degree course. It thus serves both as an excellent revision and preparation tool, and as a convenient reference source, covering the whole of theoretical physics. It may also be successfully employed to deepen its readers' insight and add new dimensions to their understanding of these fundamental concepts. Recent topics such as holography and quantum cryptography are included, thus making this a unique contribution to the learning material for theoretical physics.

Contenu

From the contents: Part I: Mechanics and Aspects of Relativity.- Space and Time.- Force and Mass.- Basic tasks of Mechanics for one-dimensional motions.-The damped and driven harmonic oscillator.- The three fundamental conservation laws.- Motion in central force fields.- The Rutherford scattering cross section.- Lagrange formalism I : The Lagrangian and the Hamiltonian.- Relativity I: Einstein's principle of the shortest proper time and Hamilton's principle of least-action momentum.- Coupled small oscillations.- Rigid bodies.- Remarks on non-integrable systems.- Lagrange formalism II: Constraints.- Accelerated reference frames.- Relativity II: E=mc².- Part II: Electrodynamics and aspects of optics.- Opening: Literature, internet, contents, purpose.- Introduction: units and (mathematical) prelimaries.- Electrostatics and magnetostatics.- Magnetic field of steady electric currents.- The general Maxwell equations I: Faraday's 'law of induction.- Maxwell's displacement current.- The general Maxwell equations II: Electromagnetic waves.- Applications of the electrodynamics in the field of optics.- Conclusion.- Part III: Quantum mechanics.- Introductory remarks.- References and internet.- On the history of quantum mechanics.- Quantum mechanics: Foundations.- One-dimensional problems.- The harmonic oscillator in the wave mechanics.- The hydrogen atom in the wave mechanics.- Abstract quantum mechanics (algebraic methods).- Spin momentum and Pauli's principle (the spin-statistics theorem).- Spin-orbit interaction.- The minimisation principle of Ritz.- Schrödinger's perturbation theory for the statics.- Time-dependent perturbations.- Magnetism as an essentially quantum-mechanical phenomenon.- Cooper pairs.- On the interpretation of quantum mechanics.- Conclusion: Repetition and summary on the history of quantum mechanics.- Looking back and looking forward.- Appendix: On cryptography and quantum cryptography.- Part IV: Thermodynamics and Statistical Physics.- Introductionand overview.- Phenomenological thermodynamics: Temperature and heat.- The fundamental theorems I and II.- Phase transitions, van der Waals theory and related problems.- Kinetic gas theory.- Statistical Physics.- From quantum statistics to the classical statistical physics.- Deepening of the fundamental theorem II.- Shannon's information entropy.- The set of canonical ensembles in the phenomenological thermodynamics.- The relation of Clausius and Clapeyron.- Generation of low and ultralow temperatures, and the fundamental theorem III.- General statistical physics (formal completion): The statistical operator and the trace formalism.- Ideal Bose and Fermi gases.- Applications I.- Applications II.- Conclusion