Module PHYS2581: FOUNDATIONS OF PHYSICS 2A

Department: Physics

PHYS2581: FOUNDATIONS OF PHYSICS 2A

Prerequisites

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

Corequisites

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

Excluded Combination of Modules

• None

Aims

• 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.

Content

• The syllabus contains:
• Quantum Mechanics: Summary of Level 1 Quantum Mechanics (the Schroedinger equation, the interpretation of the wavefunction, energy levels, plane waves); wave packets and wave packet spreading; the momentum operator; wave functions in momentum space; the delta function; the time-dependent Schroedinger equation; conservation of probability; the Ehrenfest theorem; the virial theorem; stationary states; example: the linear harmonic potential (energy levels and wave functions in terms of Hermite polynomials); general solution of the time-dependent Schroedinger equation for a time-independent potential; properties of the eigenfunctions of the Hamiltonian; introduction to the formalism of quantum mechanics (quantum states, Dirac notation, dynamical variables and operators, eigenvalues and eigenvectors, expansion in eigenfunctions, expectation values); the Schroedinger equation in 3D Cartesian coordinates; the Schroedinger equation in spherical polar coordinates for central potentials; orbital angular momentum (differential operator); eigenfunctions and eigenvalues of L2 and Lz, spherical harmonics and their properties; the hydrogen atom (calculation of the energy levels and of the bound state wave functions, radial and angular distribution functions, reduced mass); an introduction to spin, to 2-component spinors and to the addition of angular momenta; the total angular momentum J and the eigenvalues of J2 and Jz, time independent non-degenerate perturbation theory; time independent degenerate perturbation theory; example: the Stark effect in the ground state and in the n = 2 states of atomic hydrogen; quasi-degenerate states; spin-orbit coupling and the fine structure of hydrogen; hyperfine splitting.
• Electromagnetism: Electrostatics; Special Techniques; Electrostatic Fields in Matter; Magnetostatics; Magnetic Fields in Matter; Electrodynamics; Conservation Laws; Electromagnetic Waves.

Learning Outcomes

• 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.

• 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

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Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• 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 on DUO
• 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 an examination and formatively assessed through problem exercises and progress tests. The examination 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 tests 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.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Problem exercises and self-assessment; two progress tests, workshops and problems solved therein.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University