Level:Part II (yr 2)
Course Convenor:Dr E McCann
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Prior to PHYS275, the student must have successfully completed:
The student must take the following modules:
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CMod descriptionback to top
vectors and Hilbert space methods. Hermitian Operators and Dirac notation. The
position operator. Dirac delta functions and locality. The momentum picture.
The Green function for the Helmholtz equation. Commutators and functions of
Operators. Solution of Quantum Simple Harmonic Oscillator by operator methods.
Hermite polynomials. Coherent states. States in the delta-potential. Motion of
Gaussian wave packets. Scattering of packets, probability and current
densities. Potential Barrier Penetration. The propagator and Path Integral
formulation of quantum Mechanics. Representations of the Rotation group. Spin
1/2 states and solutions of the Pauli-Schrodinger equation with magnetic field
interactions. The H atom without electron spin. Ortho and Para-Hydrogen.
Multi-particle states and the coupling of angular momenta. Representations of
Permutations and the notions of identical particles, Bosons and Fermions.
Deuterons, Tritium, Ortho and Para-Hydrogen.
Curriculum Design: Outline Syllabusback to top
- revision of classical mechanics: Lagrange and Hamilton formalism
- axiomatic formulation of quantum mechanics and the Dirac notation
- states and the Hilbert space
- operators and their representations
- the time-dependent Schr¨odinger equation
- elements of measurement theory
- quantum dynamics
- unitary time evolution operator
- Schr¨odinger and Heisenberg pictures
- the density matrix
- applications of quantum dynamics
- the harmonic oscillator: operator language, coherent states,time dependence
- spin: time dependence, precession; multi-spin systems and entanglement
- symmetries in quantum mechanics
- path-integral formulation of quantum mechanics; WKB approximation and the semiclassical propagator
Educational Aims: Subject Specific: Knowledge, Understanding and Skillsback to top
The LTA strategy is fourfold. Each week the core physics material is developed in the lectures. Students are expected to reinforce and extend the lecture material by private study of the course textbook and other sources. Students understanding is consolidated and assessed via the weekly work sheet, which is completed by students independently, then marked and discussed by the lecturer at the seminar.
Learning Outcomes: Subject Specific: Knowledge, Understanding and Skillsback to top
On completion of the module, students should be able to
- set up and solve quantum problems compactly in the Dirac notation
- describe the dynamics (time dependence) of quantum systems
- apply quantum dynamics to one-dimensional systems and spin 1/2 particles
- use symmetries to reduce the complexity of quantum problems
- use semiclassical methods and concepts to
- find approximate descriptions of quantum systems and effects
- relate quantum mechanics to classical mechanics
Curriculum Design: Select Bibliographyback to top
For the module: select one (better: two) of
C Cohen-Tanoudji, B Diu and F Lalo¨e, Quantum Mechanics
F S Levin, An Introduction to Quantum Theory
R Liboff, Introductory Quantum Mechanics
J J Sakurai, Modern Quantum Mechanics
R Shankar, Principles of Quantum Mechanics, 2nd ed.
For later reference/revision
E Merzbacher, Quantum Mechanics
A Messiah, Quantum Mechanics