## Pre-requisite modules

## Co-requisite modules

## Prohibited combinations

Occurrence | Teaching cycle |
---|---|

A | Autumn Term 2019-20 to Spring Term 2019-20 |

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: **

- Interpretation of the Time-Dependent Schrödinger Equation (TDSE) and derivation of the Time-independent Schrödinger equation (TISE) from the TDSE.
- 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.
- Formal basis of quantum mechanics: the postulates of quantum mechanics; observables, Hermitian operators, and measurements; commutators and compatible observables.

**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: **

- Discuss the properties of the particles in the simplest baryon and meson multiplets

- Discuss the origin of the structure of the simplest baryon and meson multiplets
- Derive the main properties of particles from their quark sub-structure
- Explain which interactions in nature occur and which do not from knowledge of the conservation laws and the standard model.
- Discuss the standard model, including interacting bosons (W,Z) and illustrate simple reactions using Feynman Diagrams

**In Nuclear Physics, to: **

- Define nuclear binding energy and be able to do simple calculations
- 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.
- Define proton and neutron separation energy and carry out simple calculations
- Explain the concept of driplines.
- Deduce the Q-value equation for a nuclear reaction or decay process and carry out calculations based on the formulae.
- Calculate the alpha-decay lifetime and explain its dependency on energy and other nuclear variables.
- Define the concept of nuclear cross-section and relate this to a simple formula for the rate of nuclear reactions and be able to perform calculations using the formula.
- Discuss the physics of the nuclear fission and fusion processes
- Outline some of the basic properties of the nuclear force and indicate evidence for these
- Discuss the concept of exchange particles and how their mass affects the range of the force
- Outline experimental evidence for the nuclear shell model.
- Know of and be able to use the basic rules of the simple single-particle shell model to predict ground state spins and parities of odd and odd-odd nuclei
- Use the simple single-particle shell model to obtain configurations for low-lying excited states in nuclei

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 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.

*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 | Length | % of module mark |
---|---|---|

Essay/courseworkPPQs |
N/A | 14 |

University - closed examinationQuantum Physics II - Spring Exam |
1.5 hours | 43 |

University - closed examinationQuantum Physics II - Summer Exam |
1.5 hours | 43 |

None

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

University - closed examinationQuantum Physics II - Spring Exam |
1.5 hours | 43 |

University - closed examinationQuantum Physics II - Summer Exam |
1.5 hours | 43 |

**Physics Practice Questions (PPQs) -** You will receive the marked scripts via your pigeon holes. Feedback solutions will be provided on the VLE or by other equivalent means from your lecturer. As feedback solutions are provided, normally detailed comments will not be written on your returned work, although markers will indicate where you have lost marks or made mistakes. You should use your returned scripts in conjunction with the feedback solutions.

**Exams -** You will receive the marks for the individual exams from eVision. Detailed model answers will be provided on the intranet. You should discuss your performance with your supervisor.

**Advice on academic progress -** Individual meetings with supervisor will take place where you can discuss your academic progress in detail.

Rae A I M; *Quantum Mechanics* 4th 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)