# Physics and astronomy

## Quantum Mechanics 2

Module code: F3225
Level 6
15 credits in spring semester
Teaching method: Lecture
Assessment modes: Coursework, Unseen examination

This module on quantum mechanics employing Dirac notation and algebraic methods. Topics covered include:

• Dirac's formulation of quantum mechanics - bras&kets, observables, algebraic treatment of harmonic oscillator, x&p representation, compatibility, uncertainty
• Symmetries and conservation laws - generators of translations&rotations, parity, time evolution, Heisenberg picture
• Angular momentum - algebraic treatment, spin, "addition" of angular momenta, explicit form of rotation operators
• Approximation methods - time-independent perturbation theory: first and second orders, degeneracies; WKB approximation & tunneling
• Interaction picture and time-dependent perturbation theory
• Basics of field quantisation - creation and annihilation operators, EM transitions
• Basic scattering theory
• Mixed states and quantum measurement - density matrix, Bell's inequality
• Elements of relativistic QM and antiparticles

### Pre-requisite

Pre-requisites:
Level 4: (F3201) Maths Methods 1 [T1] ; (F3202) Maths Methods 2 [T2]
Level 5: (F3204) Electrodynamics [T1] ; (F3205) Maths Methods 3 [T1] ; (F3239) Quantum Mechanics 1 [T2]
Level 6: (F3211) Atomic Physics [T1]

### Module learning outcomes

• Apply algebraic approaches to selected quantum mechanical problems, in particular to angular momenta and their addition.
• Understand the principles of time-independent and time-dependent perturbation theory and apply them to simple standard situations.
• Apply differential and integral calculus to calculating properties of quantum mechanical systems.