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Theories of matter, space and time. Volume 2, Quantum theories
- Author / Creator
- Available as
- Online
- Summary
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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 Un...
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 Schrödinger 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.
Details
- Creator
- N. Evans and S.F. King
- Format
- Books
- Language
- English
- Contributors
- Publication
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- San Rafael [California] (40 Oak Drive, San Rafael, CA, 94903, USA) : Morgan and Claypool Publishers, [2018]
- Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2018]
- Series
- Physical Details
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- 1 online resource : illustrations (some color)
- data file
- ISBNs
- 9781681749839, 1681749831, 9781681749815, 1681749815, 9781681749808, 9781681749808
- OCLC
- on1044743767
- "Version: 20180601"--Title page verso.
- "A Morgan & Claypool publication as part of IOP Concise Physics"--Title page verso.
- Includes bibliographical references.
- "Professor Nick Evans completed his PhD in collider phenomenology in 1993 at Southampton University. He performed his early research work at Yale and Boston Universities in the US before returning to Southampton in 1999 on a UK government 5-year fellowship. He is now a Professor at Southampton University and the Director of the Faculty of Physical Science and Engineering Graduate School. Professor Steve King completed his PhD in QCD perturbation theory in 1980 at Manchester University. He was a postdoctoral fellow at Oxford University, where he worked on composite models, before moving to Harvard and Boston Universities in the US, where he worked on technicolour and collider phenomenology. Returning to Southampton in 1987, he won a 5-year fellowship to work on lattice QCD and top quark condensates. He is now Professor and First Year Director of Studies in Physics and Astronomy at Southampton.
- 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