PHYS2581: FOUNDATIONS OF PHYSICS 2A

• Foundations of Physics 1 (PHYS1122) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus I (MATH1061) and Linear Algebra I (MATH1071))).

• Mathematical Methods in Physics (PHYS2611) OR Analysis in Many Variables II (MATH2031) which covers similar material

• None

• This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes
• It builds on the Level 1 module Foundations of Physics 1 (PHYS1122) by providing courses on Quantum Mechanics and Electromagnetism.

• The syllabus contains:
• Quantum Mechanics: Review of Level 1 quantum mechanics, wavefunction normalisation and expectation values, operators and non-commutative algebra [x,p]=-i hbar, time independent Schroedinger equation and general solution, properties of eigenfunctions (span the space, orthonormal), review of simple central potentials, generalized statistical interpretation, commuting operators, common eigenfunctions, 3D potentials in cartesian and spherical coordinates, angular momentum operators, spherical harmonics and vector model for L^2 and L_z, hydrogen wavefunctions and energies - transitions, generalised angular momentum and electron spin, nondegenerate perturbation theory, degenerate perturbation theory, application to hydrogen I - spin orbit coupling, adding angular momentum, application to hydrogen II - relativistic corrections and total fine structure, application to hydrogen III - lamb and hyperfine corrections, meaning of quantum mechanics Schroedinger's cat.
• Electromagnetism: Divergence and Curl of Electrostatic Fields, Conductors. Electrostatic Fields in Matter: Polarization, The Electric Displacement, Linear Dielectrics. Magnetostatics: The Lorentz Force Law, The Biot-Savart Law, The Divergence and Curl of B, Magnetic Vector Potential. Magnetic Fields in Matter: Magnetization, The Auxiliary Field H, Linear Media. Electromotive Force, Electromagnetic Induction, Maxwell's Equations. Conservation Laws: Charge and Energy. Electromagnetic Waves: Waves in One Dimension, Electromagnetic Waves in Vacuum, Electromagnetic Waves in Matter, Absorption and Dispersion, Guided Waves.

Subject-specific Knowledge:

• Having studied the module students will be familiar with the formal theory of quantum mechanics and have an ability to use the theory to solve standard problems for model systems
• They will have a quantum mechanical understanding of the basic properties of the hydrogen atom and be able to use quantum theory to calculate various aspects of physical behaviour
• They will be able to carry out simple quantum mechanical calculations using the variational method and time-independent perturbation theory
• They will be familiar with and able to manipulate and solve Maxwell's equations in a variety of standard situations
• They will have an understanding of how the electrical and magnetic properties of simple media can be represented, and an appreciation of the key concepts relating to the propagation and radiation of electromagnetic waves in free space and simple media.

Subject-specific Skills:

• In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of predictable and unpredictable problems
• They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation

Key Skills:

• Teaching will be by lectures and tutorial-style workshops
• The lectures provide the means to give concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of the recommended textbooks for the module, thus making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online
• Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills
• Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times
• Student performance will be summatively assessed through a written examination and an online test and formatively assessed through problem exercises and a progress test. The written examination and online test will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The problem exercises, progress test and workshops will provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.

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