## Pre-requisite modules

## Co-requisite modules

## Prohibited combinations

Occurrence | Teaching period |
---|---|

A | Autumn Term 2022-23 to Spring Term 2022-23 |

The quantum mechanics moves on from the initial description in Quantum Physics I, introducing the time dependent Schrödinger equation and the relationship between this and the time-independent Schrödinger equation. Simple 1-, 2- and 3- dimensional physical systems are developed using Schrödinger's equation. It is shown how observable quantities such as position and momentum are represented by Hermitian operators. The properties of these operators are studied. The expansion theorem is introduced and its interpretation in relation to the theory of measurement. The theory is related to observations whenever possible.

The module continues with atomic physics where the principal aim is to impart a basic knowledge of atomic structure, and to illustrate how atomic structure is interpreted from the measurement of spectra. The classical Bohr and Bohr-Sommerfeld theories and semi-classical vector model of atomic structure are applied to the hydrogen atom. These simple models extend to describe the general one-electron atom. The module covers the concepts of core electron screening and valence electron penetration and introduces the quantum defect. The discussion moves to interpretation of the Stern-Gerlach experiment and introduces electron spin and fine structure. Methods for measuring optical and X-ray spectra, and the observation and interpretation of the Zeeman effect are outlined.

The module then continues with particle physics where the goal is to give a simple overview of the standard model. The main properties of particles from their quark sub-structure to the simplest baryons and meson multiplets will be examined.

The module progresses onto nuclear physics and begins by examining aspects of two out of the four forces of nature. It examines first the mass and energy relationships of the atomic nucleus and the semi-empirical mass formula. Nuclear decay properties are then studied before moving onto nuclear reactions. The interactions of nucleons and the basic properties of the strong nuclear force are then examined culminating in the exploration of the simple shell model of the atomic nucleus.

**In Quantum Mechanics, to: **

- Interpret the Time-Dependent Schrödinger Equation (TDSE) and derive the Time-independent Schrödinger equation (TISE) from the TDSE.
- Determine and apply operators to calculate eigenfunctions, eigenvalues, and expectation values for one-, two- and three-dimensional quantum systems.
- Determine the time-dependency of particles in one-, two- and three-dimensional quantum systems.
- Apply this understanding to particles in potentials, whether it be a spherical symmetry or reflection symmetry, and discuss the quantum numbers arising from these symmetries.
- Relate the behaviour of quantum systems to the formal basis of quantum mechanics, the postulates of quantum mechanics.

**In Atomic Physics, to: **

- Give brief accounts of atomic physics models.
- Define degeneracy, and calculate the degeneracy in atomic systems.
- Describe the origin of optical and X-ray spectral line emission.
- Use and interpret spectroscopic notation.
- Illustrate how spectroscopic measurements are made.
- Construct, label, and compare energy level diagrams.
- Apply the selection rules.
- Perform calculations for simple atomic systems.

**In Particle Physics, to: **

- Describe the standard model, including fermions and interaction bosons, as well as their interaction in the simplest Feynman-diagram vertices.
- Derive the main properties of the simplest baryons and mesons from their quark sub-structure and discuss the origin of this structure.
- Discuss the properties of leptons, and illustrate decays of leptons and leptonic decay modes of particles using Feynman Diagrams.
- Determine the conservation laws observed in standard-model reactions and decays based on knowledge of Feynman Diagrams.
- Discuss the link between the dominant decay modes of hadrons and their quark structure and determine one from the other for the simplest baryons and hadrons.
- Discuss the significance of fundamental and composite standard model particles in the context of atomic and nuclear quantum systems.

**In Nuclear Physics, to: **

- Define the terms in the semi-empirical mass formula and be able to use it to explain the chart of the nuclides and perform calculations.
- Discuss and apply the key physics concepts of the nuclear reaction and decay processes, including nuclear fission; fusion; alpha decay lifetimes; beta decay; and cross sections.
- Define and determine the energy involved in reactions and other nuclear processes, and apply this to examples such as binding energy, Q-value, separation energy, while linking these to the stability of nuclei and drip lines.
- Outline experimental evidence for the nuclear shell model, know and be able to use the basic rules of the single-particle shell model to predict quantum mechanical properties of nuclei and their excited states.
- Outline some of the basic properties of the nuclear force, indicate evidence for these, and discuss these properties in the context of exchange particles and their masses.

Note - In addition to module listed above, students should either have taken PHY00022C or PHY00026C as prerequisite modules.

*Quantum Mechanics*

- Formal basis of quantum mechanics: the postulates of quantum mechanics; observables, Hermitian operators, and measurements; commutators, compatible observables, and the uncertainty principle.
- Interpretation of the Time-Dependent Schrödinger Equation (TDSE) and solutions of the TDSE using separation of variables.
- Operators and observables: position and momentum operators; the Hamiltonian operator; angular momentum operators; eigenfunctions, eigenvalues, and expectation values.
- The simple harmonic oscillator (SHO); solutions of the TISE; energy eigenvalues and eigenfunctions for the SHO
- Particle in a two- and three-dimensional box and in the three-dimensional harmonic oscillator potential; energy eigenvalues and eigenfunctions; degeneracy table; accidental and symmetry degeneracy.
- Particle in a spherically symmetric potential; the TISE in spherical polar coordinates; the hydrogenic wavefunctions and energy eigenvalues. Eigenfunctions and eigenvalues of the angular momentum operator.

*Atomic Physics*

- Atomic spectra
- Bohr and Bohr-Sommerfeld theories
- The vector model of angular momenta
- Stern-Gerlach experiment and electron spin
- Fine structure
- A summary of the quantum numbers
- One electron atoms and the quantum defect
- Energy diagrams, allowed transitions and selection rules
- X-ray emission and Moseley's Law
- The Zeeman effect

*Particle Physics*

- Standard Model concepts. Classification of fundamental and composite particles: hadrons (baryons and mesons), leptons, exchange particles, and spins.
- Brief outline of main interactions seen in nature: The Strong, Weak, Electromagnetic and Gravitational Interactions and their properties.
- An introduction to conservation laws including spin, isospin, strong hypercharge and lepton number, as well as their relationship to Feynman diagrams as a descriptor of reactions and decay-processes in particle physics.
- The relationship between the lifetime of a particle; the width of a particle resonance (as observed in a particle physics experiment); and the available decay modes of the particle.
- Fundamental and composite particles in atoms and nuclei, including muonic atoms, positronium, and particles as mediators of nuclear and atomic forces and decays.

*Nuclear Physics*

- Basic definitions and concepts: masses; radii; and nuclear binding energy.
- Gross properties of nuclei: semi-empirical mass formula; nuclide chart; limits of stability; neutron/proton separation energies; and drip lines.
- Unstable nuclei: decay and radioactive dating; kinematics and Q-value for alpha and beta decay; and gamma decay of excited nuclear states.
- Quantum tunnelling for alpha-decay: derivation tunnelling probability and evaluation of the impact on alpha decay lifetimes.
- Nuclear reactions: kinematics and notation; definition of types of reaction, elastic, inelastic, and capture; reaction cross-sections; and Q-value for reactions.
- Evidence for shell structure in nuclei; introduction to the simple single-particle nuclear shell model and its use to predict ground state and excited state spins and parities, brief discussion of the regions where the shell model approach is valid and reasons for its failure.
- Fission: physics of the fission process, prompt and delayed neutrons, fission and the liquid drop model, definitions of spontaneous, induced fission and activation energy.
- Fusion: - Physics of nuclear fusion, particularly hydrogen fusion; and discussion of cross-sections and reaction rates.

Task | % of module mark |
---|---|

Closed/in-person Exam (Centrally scheduled) |
40 |

Closed/in-person Exam (Centrally scheduled) |
40 |

Essay/coursework |
10 |

Essay/coursework |
10 |

None

Task | % of module mark |
---|---|

Closed/in-person Exam (Centrally scheduled) |
50 |

Closed/in-person Exam (Centrally scheduled) |
50 |

Our policy on how you receive feedback for formative and summative purposes is contained in our Department Handbook.

RA I M; *Quantum Mechanics*, e.g. 6th Ed (McGraw-Hill)*** (*Quantum Mechanics)*

Eisberg R M & Resnick R; *Quantum Physics of Atoms, Molecules, Solids, Nuclei and Particles* (Wiley)*** (*Atomic Physics/Quantum Mechanics)*

Krane K S: *Introductory nuclear physics* (Wiley) *** (Nuclear Physics)

Hughes I S: *Elementary particles* (Cambridge) *** (Particle Physics)