Topics covered: time-independent perturbation theory, non degenerate and
degenerate cases, fine structure of the hydrogen atom, variational principle,
helium atom, H2 ion, WKB approximation, tunneling, time-dependent perturbation
theory, emission and absorption of electromagnetic radiation, scattering,
The aim of this
course is to consolidate and extend your knowledge of quantum mechanics by
introducing more theoretical tools and some more advanced applications.
By the end of this
course, the student should be able to:
§ Extend quantum theory to three dimensions using the
machinery of angular momentum for systems with spherical symmetry.
§ Discuss the spin or formalism to describe physical
spin and two-level systems.
§ Compute the dynamical evolution of quantum systems and
convert results between the different representations of quantum theory.
§ Describe independent quantum systems, including
identical particles, and give their quantum information content.
§ Examine in detail a number of key experiments relating
to the quantum theory.
§ Apply Schrödinger’s equation to determine advanced
problems in quantum mechanics.
completing the course is expected to demonstrate knowledge and understanding
§ operators and
states using Dirac's bra and ket notation
§ simple harmonic
oscillator using raising and lowering operators
§ quantum angular
momentum, including spin, and analyse it using raising and lowering operators
§ non-locality and
the Bell inequalities, and apply the concepts to cryptographic key exchange
§ qubits and some
basic ideas in quantum computation
§ WKB approximations