Advanced Quantum Physics

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Be able to work with operators and states using Dirac's bra and ket notation
• Study the simple harmonic oscillator using raising and lowering operators
• Understand qubits and some basic ideas in quantum computation and quantum decoherence
• Understand Lorentz invariant formulation of Quantum Mechanics
• Understand non-locality and the Bell inequalities, and apply the concepts to cryptographic key exchange
• Understand quantum angular momentum, including spin, and analyse it using raising and lowering operators

CHAPTER 1: MATHEMATICAL TOOLS (vector spaces and Dirac notation)

CHAPTER 2: THE PRINCIPLES OF QUANTUM MECHANICS

CHAPTER 3: HARMONIC OSCILLATOR IN QUANTUM MECHANICS (using ladder operators)

CHAPTER 4: ANGULAR MOMENTUM

* Definition, ladder operators, general results

* Orbital angular momentum

* Spin angular momentum

* Adding angular momenta

* Clebsch-Gordan coefficients

* Entangled states

CHAPTER 5: RELATIVISTIC QUANTUM MECHANICS (Klein-Gordon equation, Dirac equation)

CHAPTER 6: THE SECOND QUANTUM REVOLUTION

* Bell inequalities (EPR paradox, spin correlation measurements, Bell's inequality)

* Basic ideas of Quantum computing (qubits, quantum teleportation)

* Quantum cryptography (distributing secure keys)

* Quantum decoherence (density matrix and Schroedinger's cat paradox)

Resources & Reading list

Textbooks

JJ Sakurai (1994). Modern Quantum Mechanics. Addison Wesley.

S Gasiorowicz (1996). Quantum Physics. John Wiley.

RP Feynman et al (1970). Feynman Lectures on Physics. Addison Wesley.

R Shankar (1994). Principles of Quantum Mechanics. New York: Plenum Press.

Assessment strategy

Weekly problem sheets will be set, three of which will be assessed with the worst one waived. 1 mini-dissertation on Chapter 6 will be assigned at the end of the last week before the Christmas break with deadline at the end of the week after the Christmas break.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.

Repeat Information

Repeat type: Internal & External