This module aims to develop an intermediate-level understanding of quantum mechanics, including familiarity with its mathematical formulation. It is intended to bridge the gap between the qualitative, pictorial approach used in the core modules of the first two years and a rigorous mathematical formulation of both time-independent and time-dependent quantum mechanics. A combination of lecture-based teaching, self-study, and problem-based learning will be used. Key concepts and tools will be presented in lectures, while regular workshops and informal self-study sessions will lead the students to applying them to real problems relevant to chemistry and to modern spectroscopic techniques such as magnetic resonance and magnetic resonance imaging.
Aims and Objectives
Having successfully completed this module you will be able to:
- understand their formulation in mathematical terms
- understand the quantum mechanical treatment of angular momentum
- use time-dependent quantum mechanics to understand magnetic resonance and magnetic resonance imaging.
- understand the fundamentals of quantum mechanics
- understand the role of time in quantum mechanics
- predict atomic and molecular spectra taking electron and nuclear spin into account
- understand how quantum states of multiple identical particles combine and how spin isomers arise.
- use time-dependent quantum mechanics to predict the outcome of simple experiments
Part A: The Quantum World
Time independent quantum mechanics
1. Operators, momentum, commutators, expectation values
2. Heisenberg’s uncertainty principle, Schrödinger equation
3. Angular momentum, commutation, raising and lowering operators, quantisation of angular momentum
5. Fine structure and hyperfine structure
6. Coupling of angular momenta. Singlet and triplet states
7. Two particles in a box: The Pauli principle and the Pauli exclusion principle.
8. Multielectron atoms.
9. The allotropes of H2: Ortho and parahydrogen
Part B: How Spins, Atoms, and Molecules Move
10. Time-dependent quantum mechanics: Schrödinger equation
11. Time evolution of stationary states.
12. Superposition states. Quantum paradoxes - Schrödinger’s cat & friends
13. Spin state precession, magnetic resonance, and magnetic resonance imaging.
Learning and Teaching
Teaching and learning methods
Study time allocation [Contact time includes: Lectures, seminars, tutorials, project supervision, demonstration, practicals/workshops/fieldwork/external visits/work based learning]
Teaching and Learning Methods
Formal lectures will provide an introduction to each of the topics covered by the syllabus and will include worked examples and illustrations of applications of the concepts.
Workshops will provide students with guided practice in application of the concepts covered by the syllabus that exemplify the theories covered and will allow students to deepen their understanding.
Self-study will enable students to consolidate their knowledge of the subject matter and to explore the application of the concepts to additional problems.
|Practical classes and workshops||8|
|Preparation for scheduled sessions||32|
|Total study time||150|
Resources & Reading list
M. H. Levitt (2007). Spin Dynamics. Wiley.
P. W. Atkins and R. S. Friedman (2011). Molecular Quantum Mechanics. OUP.
C. Cohen-Tannoudji, B. Diu, F. Laloe (1977). Quantum Mechanics. Wiley.
Summative assessment description
Referral assessment description
Repeat type: Internal & External