Module manager: Prof. Jiannis Pachos
Email: J.K.Pachos@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2026/27
Level 6 Physics or equivalent
| PHAS3400 | Advanced Quantum Physics |
This module is not approved as an Elective
Build on prior quantum physics to develop a working toolkit for real systems. Topics include matrix mechanics and spin, approximation methods (variational, degenerate and time-dependent perturbation theory), and quantum dynamics of charged particles in magnetic fields (Aharonov–Bohm, Landau levels, quantum Hall). Through problem-solving and applications, students will bridge theory and experiment and prepare for advanced modules and research.
At the end of this module students should be able to:
- State and use the postulates of quantum mechanics in Dirac/matrix form; evaluate commutators, expectation values and uncertainties.
- Solve separable Schrödinger problems and treat charged particles in uniform magnetic fields (Landau levels).
- Analyse spin-1/2 and two-level systems with Pauli matrices; change basis, diagonalise operators and interpret measurements.
1) Formulate and analyse spin-½ or two-level Hamiltonians with Pauli matrices; diagonalise and predict dynamics.
2) Model charged particles in magnetic fields and derive Landau levels and degeneracies.
3) Apply the variational principle with justified trial states to bound energies.
4) Use time-independent (incl. degenerate) and time-dependent perturbation theory to compute corrections and transition rates.
Skills Learning Outcomes
a) The ability to use quantum mechanics in different scientific disciplines (chemistry, biology, etc.) and apply the same mathematics in other fields.
b) Solve unseen quantitative problems and justify assumptions in clear, structured arguments.
Postulates of quantum mechanics and Dirac notation: operators, commutators, measurement.
Separable solutions of the Schrödinger equation (Cartesian); infinite wells and periodic boundary conditions.
Harmonic oscillator via ladder (creation/annihilation) operators.
Charged particles in uniform magnetic fields: vector potentials, gauges, Landau quantisation and degeneracy.
Integer quantum Hall effect (qualitative): Landau levels, edge states, Hall conductance.
Variational principle: energy bounds from trial wavefunctions.
Time-independent perturbation theory (non-/degenerate): energy/state corrections, selection rules.
Time-dependent perturbation theory: transition probabilities and Fermi’s Golden Rule.
Matrix mechanics and spin systems: Pauli matrices, two-level Hamiltonians, dynamics and measurements.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 27 | 1 | 27 |
| Private study hours | 123 | ||
| Total Contact hours | 27 | ||
| Total hours (100hr per 10 credits) | 150 | ||
123 Private Study Hours
Feedback on coursework
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Last updated: 30/04/2026
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