- Department: Physics
- Credit value: 20 credits
- Credit level: H
- Academic year of delivery: 2022-23
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
Occurrence | Teaching period |
---|---|
A | Autumn Term 2022-23 to Spring Term 2022-23 |
This course aims to introduce advanced topics and techniques in quantum mechanics, and links these to relevant applications in nuclear physics and our description of the structure of the atomic nucleus.
On the quantum mechanics side, the course aims to:
In terms of nuclear physics, this module will focus on advanced topics and begin to examine how these topics are addressed in contemporary nuclear physics research. We will examine the key models that underpin nuclear structure – associated with both “single-particle” and “collective” modes of excitation. The module then aims to develop understanding of the quantum mechanical mechanisms underlying nuclear decays and, hence, to examine what nuclear structure information can be extracted from such measurements. The physics of nuclear fission and fusion will be discussed as well as the principles of operation of fission and fusion reactors. In all of the above, published data will be used regularly to illustrate and test the ideas presented.
Quantum mechanics:
- understand the physical significance of commutators in terms of compatibility of measurements
- Perform simple commutator algebra, in order to obtain commutators for operators expressible in terms of the position and momentum operators.
- Derive operators for the angular momentum components Lx, Ly, Lz, and for L2, in terms of position and momentum operators in Cartesian coordinates
- Understand how the angular momentum operators are transformed from Cartesian into spherical polar coordinates
- Derive the operators for Lz and L2 in spherical polar co-ordinates
- Derive and interpret the eigenvalues and eigenvectors of the operators for angular momentum, Lz, and L2 in terms of possible measurement results.
- Explain the use of the central force theorem for a spherically symmetric potential within the context of the time-independent Schrödinger equation written in spherical polar co-ordinates and applied to hydrogen-like atoms
- Discuss the relationship between the operators Lz L2 and the above Hamiltonian for a hydrogen-like atom system
- Apply the above to solving the full analytical eigensolution for the case of the Hydrogen atom, as well as sub-components of this eigenproblem
- Reproduce and interpret a labelled diagram showing the energy levels and angular momentum states of the hydrogen atom
- Provide a physical interpretation of the quantum numbers n, l and ml and be able to sketch the wavefunction solutions of the hydrogen atom for a given n, l and ml)
- Understand the matrix formalism of quantum mechanics and apply this to the case of spin
- Apply the Pauli spin matrices to find the eigenvalues and eigenvectors of spin operators
- Interpret generalised Stern-Gerlach experiments in terms of eigenvector superposition, illustrating the theory of measurement.
- Derive the first and second order energy corrections in non-degenerate perturbation theory and apply the formulae to simple problems e.g. anharmonic oscillators
- Learn of other approximate methods such as the matrix eigenvalue formalism for degenerate perturbation theory and make applications to simple systems e.g. Stark effect in Hydrogen, as well as the variational approach.
Nuclear physics:
- Describe the significance of nuclear charge and current distributions in regard to nuclear structure and decays
- Discuss the variety of mechanisms that result in the generation of excited states in nuclei.
- Predict angular momentum and parity quantum numbers of excited states in nuclei, based on nucleonic single-particle configurations.
- Interpret aspects of published level schemes in terms of both single-particle and collective models, demonstrating how information on the different types of excitation are extracted from the data.
- Discuss the quantum-mechanical basis for the three modes of nuclear decay.
- Describe the key models and methods used to predict nuclear decay rates.
- Perform sample calculations of alpha, beta and gamma-decay rates, based on the models presented
- Interpret nuclear decay data, through an understanding of these models, in terms of nuclear structure phenomena.
- Discuss the physics of the nuclear fission and fusion processes
- Define what is meant by prompt and delayed neutrons, spontaneous and induced fission and activation energy and be able to predict whether isotopes with fission with thermal neutrons.
-Explain the basics of how thermal fission reactors operate
Please note, students who have not taken the prerequisites listed above must have taken an equivalent version of Quantum Physics II and Mathematics II.
Syllabus
Quantum mechanics:
Nuclear Physics:
Nuclear moments:
Nuclear models:
Alpha decay:
Gamma-ray decay:
Beta decay:
Fission:
Fusion:
Task | % of module mark |
---|---|
Essay/coursework | 20 |
Essay/coursework | 30 |
Essay/coursework | 20 |
Essay/coursework | 30 |
None
Task | % of module mark |
---|---|
Essay/coursework | 20 |
Essay/coursework | 30 |
Essay/coursework | 20 |
Essay/coursework | 30 |
Our policy on how you receive feedback for formative and summative purposes is contained in our Department Handbook.
A I M Rae: Quantum mechanics (McGraw-Hill) ***
R C Greenhow: Introductory quantum mechanics (Taylor & Francis/IoP Publishing) **
B H Bransden and C J Joachain: Introduction to quantum mechanics (Prentice Hall)*
Krane K S: Introductory nuclear physics (Wiley) ****
Heyde K: Basic ideas and concepts in nuclear physics (Taylor & Francis/IoP Publishing) **
Burcham W E and Jobes M: Nuclear and particle physics (Prentice Hall/Longman) **
Lilley J: Nuclear physics principles and applications (Wiley) **