PH22006: Foundations of physics 2
[Page last updated: 03 June 2024]
| Academic Year: | 2024/25 |
| Owning Department/School: | Department of Physics |
| Credits: | 20 [equivalent to 40 CATS credits] |
| Notional Study Hours: | 400 |
| Level: | Intermediate (FHEQ level 5) |
| Period: |
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| Assessment Summary: | EXCB 50%, EXOB 50% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| Requisites: |
Before taking this module you must take PH12002
While taking this module you must take PH22010 |
| Learning Outcomes: |
After taking this unit the student should be able to:
explain the significance of the wavefunction in determining the physical behaviour of electrons;
show how quantisation arises from boundary conditions and calculate energy levels in simple model systems;
discuss the energy levels, angular momenta and spectra of atoms, taking into account screening and magnetic interactions;
justify the need for a microscopic approach to thermal physics and demonstrate an understanding of the microstate formalism;
derive the appropriate thermodynamic potentials from the partition function of simple models;
describe the Fermi-Dirac, Bose-Einstein, Boltzmann and Planck distribution functions and apply them to simple models;
outline the ways in which crystal structures are described formally and relate structures in real space to those in reciprocal space;
describe how allowed and forbidden energy bands arise as a result of crystal potentials and how the properties of electrons in allowed energy bands determine the electrical and optical behaviour;
describe classical theories of diamagnetism, paramagnetism, and the ferromagnetic properties of materials;
derive and interpret Maxwell's equations and their solution in vacuum;
analyse in detail the propagation of vectorial plane waves in vacuum and in various materials;
describe the origins of polarisation and magnetisation in materials. |
| Synopsis: | Building on Foundations of Physics 1, you will deepen your knowledge of key concepts underpinning our understanding of the physical world. You'll learn how quantum theory is built from a set of fundamental postulates that enable you to understand the properties of atoms and solids, how Maxwells equations unify the laws of electricity & magnetism and explain the properties of electromagnetic waves, and how simple counting rules make fundamental sense of the concepts of temperature and entropy. |
| Content: | Atomic physics & matrix mechanics (24 lecture hours): Matrix mechanics, Dirac notation. Old models of the atom; the Schroedinger hydrogen atom: Angular wavefunction, radial wavefunction, full solutions, energy and atomic spectra, electronic states of many electron atoms, Pauli exclusion principle. Angular momentum in atoms: Orbital angular momentum, spin angular momentum, Dirac notation, superposition, Pauli spin. Magnetic properties of atoms: Magnetic moments, total angular momentum, spin-orbit interaction, perturbation theory, Zeeman effect and Stern Gerlach experiment.
Statistical mechanics (14 lecture hours): Macroscopic and microscopic approaches to thermal physics. Introduction to statistical mechanics: Microstates. Energy degeneracy. Multiparticle systems. Indistinguishability. Ensemble average. Statistical ensembles. Interacting systems. Temperature. Entropy. Chemical potential. Thermodynamic identity. Postulates and laws of thermodynamics. Boltzmann distribution and ideal gas: Partition function. Boltzmann distribution. Partition function for many particles. Equipartition theorem. Density of states. Particle in a box. Maxwell-Boltzmann distribution. Velocities of particles in a gas. Ideal monoatomic gas. Fermi and Bose gases: Grand-canonical distribution. Fermi gases. Fermi-Dirac distribution. Classical and Quantum statistics. Fermi energy. Fermion gas law. Bose Einstein distribution. Bose-Einstein condensation. Bose gases. Boson gas law. Experiments on atom cooling and Bose condensation. Photon gas. Phonon gas. Heat capacity of an insulating solid.
Condensed matter physics (22 lecture hours): Crystal structures: Diffraction of waves in crystalline structures; Bragg law, the reciprocal lattice and Brillouin zones. X-ray and neutron diffraction studies of crystal structures. Electrons in solids: Classical Drude theory and its failures. The Hall effect. Quantum (Sommerfeld) theory. Density of states and the Fermi sphere. The effect of crystalline periodicity. Energy band diagrams and effective masses. The distinction between metals, semiconductors and insulators. Semiconductors: Holes. Basic properties of intrinsic semiconductors; H-model of doped semiconductors, donors and acceptors; p-n junction. Magnetism: Magnetic susceptibility. The origin of magnetic moments in solids. Classical models of diamagnetism and paramagnetism. Ferromagnetism and the exchange interaction. Lattice dynamics: Optical and acoustic vibrations. Phonons. Classical and quantum theories of heat capacity.
Maxwell's equations (20 lecture hours): Introduction to Maxwell's equations: Derivation of integral and differential forms of Maxwell's equations and continuity equation. The wave equation in source-free vacuum. Plane wave solutions. Electromagnetic plane waves: 3D plane waves, vector nature of electromagnetic wavesl relationships between E, B and k. Impedance. Electromagnetic energy and the Poynting vector. Radiation pressure. Polarisation; Law of Malus, circular and elliptical polarisation. Birefringence, wave plates. Maxwell's equations in infinite materials: Concepts of linearity, isotropy and homogeneity. Characterisation of materials in terms of macroscopic parameters. Dipoles, susceptibility and polarisation / magnetisation. The modified wave equation; solution in conductors, dielectrics, lossy media and plasmas. Boundaries between media: The general electromagnetic boundary conditions. Plane waves at a planar boudary, general angle of incidence (Fresnel equations). Total internal reflection and evanescent waves. Coefficients of transmission and reflection. Brewster and critical angles. Lasers: Interaction between light and matter. The Einstein relations. Obtaining and maintaining lasing action. Cavity modes. The properties of laser light. |
| Course availability: |
PH22006 is a Must Pass Unit on the following courses:Department of Physics
PH22006 is Compulsory on the following courses:Department of Chemistry
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Notes:
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