## PHYS4013 Physics Honours Coursework A

## Lecturer(s):

**Quantum Mechanics**

Prof Oleg Sushkov (weeks 1-3)

A/Prof Michael Kuchiev (weeks 4-5)

A/Prof Clemens Ulrich (weeks 6-8)

**Electrodynamics and the Standard Model**

A/Prof Michael Kuchiev

## Course Description :

Advanced topics in quantum mechanics and electrodynamics and the standard model

**Quantum Mechanics**

Identical particles, fermions and bosons.

Born-Oppenheimer approximation for molecules and solids.

Classification of electronic states of diatomic molecules.

Charged particle in magnetic field. Landau levels.

Heisenberg formulation of Quantum Mechanics. Creation/annihilation operators for harmonic oscillator.

Electron in periodic potential, band structure, 1D example, quasimomentum.

Surface states articulated in terms of the band structure. Concept of pseudospin.

Graphene, 2D Dirac equation. Spin-orbit interaction, topological insulators and topological protection.

Relativistic equations: Klein-Gordon equation, Dirac equation.

Scattering Theory: Scattering amplitude, Born approximation, Low-energy scattering, scattering phases,

resonance scattering.

Scattering of ultrarelativistic electrons, helicity conservation.

Analogy between scattering of ultrarelativistic electrons and scattering in graphene.**Electrodynamics and the Standard Model**

Vector potential, tensor of EM field,

Gauge invariance,

Action of a particle in an EM field and action of an EM field, Lagrangian.

Equations of motion – Maxwell’s equations, and equation for a charged particle

(Examples: electron in static electric or/and magnetic fields, electron in an electromagnetic wave).

Liénard - Wiechert retarded potentials and fields.

Radiation from an accelerated particle: synchrotron radiation, spectrum, polarization and angular

distribution; dipole radiation.

Scattering of EM waves: long-wave limit and short wave limit

Dirac monopoles, quantization condition, dyons.

Idea of non-Abelian gauge invariance and mathematical structure of the standard model.

Idea of the Higgs mechanism for generation of masses. Why Higgs mechanism is necessary,

the concept of renormalizability.

## Semester(s) Offered:

Semester 1 only