MAU34403 Quantum mechanics I
| Module Code | MAU34403 |
|---|---|
| Module Title | Quantum mechanics I |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Sergey Frolov |
| Module Prerequisites | MAU23402 Advanced classical mechanics II |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1.
- Continuous assessment contributes 10% towards the overall mark.
- Re-assessment, if needed, consists of 100% exam.
Contact Hours
11 weeks of teaching with 3 lectures and 1 tutorial per week.
Learning Outcomes
On successful completion of this module, students will be able to
- State the basic postulates of quantum mechanics.
- Derive the general Schrödinger and Heisenberg equations of motion.
- Use symmetries to simplify complex problems.
- Apply quantum theoretical techniques to complex problems.
- Demonstrate an entry-level understanding of 20th and 21st century physics.
Module Content
- Mathematics of quantum mechanics: Bras and kets, Spin-1/2 representation of su(2), Hilbert spaces, creation and annihilation operators, Hermitian operators, tensor product, coordinate representation and momentum representation of the Heisenberg algebra.
- Postulates of quantum mechanics: States, observables, measurements, probabilities and amplitudes, quantum dynamics, the Heisenberg picture and the Schrödinger picture, symmetries in quantum mechanics.
- Simple problems in various dimensions: Free particles, harmonic oscillator, bounded potential in one dimension, scattering in one dimension, separation of variables, Pauli equation, charged particle in a magnetic field, Aharonov-Bohm effects.
- Angular momentum and central field: Irreducible representations of su(2), tensor product of irreducible representations, orbital angular momentum eigenfunctions, radial Schrödinger equation, Gross structure of hydrogen.
Recommended Reading
- Principles of quantum mechanics by Shankar.
- Modern quantum mechanics by Sakurai.
- The physics of quantum mechanics by Binney and Skinner.
- Introduction to quantum mechanics by Griffiths.
- Lectures on quantum mechanics for mathematics students by Faddeev and Yakubovskii.
- Quantum mechanics by Merzbacher.