Theories of matter, space and time. Volume 2, Quantum theories / N. Evans and S.F. King.

Περιλαμβάνει βιβλιογραφικές παραπομπές.

1. Non-relativistic quantum mechanics -- 1.1. One dimensional, time dependent Schrödinger equation -- 1.2. Time independent Schrödinger equation -- 1.3. Interpretation -- 1.4. Proof that probability is conserved -- 1.5. Momentum space wave functions -- 1.6. Heisenberg uncertainty principle -- 1.7. Square well example -- 1.8. Completeness -- 1.9. Orthogonality -- 1.10. The 3D Schrödinger equation -- 1.11. Wave function collapse and all that

Appendix A. Time independent perturbation theory -- A.1. Example : perturbed square well -- Appendix B. Orbital and spin angular momentum

2. Path integral approach to quantum mechanics -- 2.1. Proposal for the quantum mechanical amplitude -- 2.2. The classical limit -- 2.3. Wave functions -- 2.4. Deriving the Schrödinger equation -- 2.5. Path integral for a free particle -- 2.6. Interpreting the free particle kernel -- 2.7. Barrier problems -- 2.8. The kernel in terms of wave functions

Appendix C. Gaussian integrals -- Appendix D. Scattering theory -- D.1. Traditional time dependent perturbation theory -- D.2. Initial response to a perturbation -- D.3. Example : perturbed square well II -- D.4. Fermi's golden rule

3. Relativistic quantum mechanics -- 3.1. Relativity review -- 3.2. The Klein-Gordon equation -- 3.3. Dirac equation

4. Quantum electrodynamics -- 4.1. Photon wave equation -- 4.2. Minimal substitution -- 4.3. Gauge invariance -- 4.4. QED interactions in perturbation theory -- 4.5. Cross sections and decay rates -- 4.6. More scattering processes -- 4.7. Renormalization -- 4.8. g -2 of the electron.

This book and its prequel Theories of Matter Space and Time: Classical Theories grew out of courses that we have both taught as part of the undergraduate degree program in Physics at Southampton University, UK. Our goal was to guide the full MPhys undergraduate cohort through some of the trickier areas of theoretical physics that we expect our undergraduates to master. Here we teach the student to understand first quantized relativistic quantum theories. We first quickly review the basics of quantum mechanics which should be familiar to the reader from a prior course. Then we will link the Schr�odinger equation to the principle of least action introducing Feynman's path integral methods. Next, we present the relativistic wave equations of Klein, Gordon and Dirac. Finally, we convert Maxwell's equations of electromagnetism to a wave equation for photons and make contact with quantum electrodynamics (QED) at a first quantized level. Between the two volumes we hope to move a student's understanding from their prior courses to a place where they are ready, beyond, to embark on graduate level courses on quantum field theory.