The postulates of Quantum Mechanics, [Mathematical background] Complex vector spaces and scalar products, linear forms and duality, the natural scalar product derived from linear forms, Hilbert spaces, linear operators, commutation relations, expectation values, uncertainty, [Time evolution and the Schrodinger equation] Derivation of the Schrodinger equation for time-independent Hamiltonians, the position and momentum representations, the probability current, the free particle [The Hydrogen atom] Quantization of energy and angular momentum, general treatment of central potentials in terms of spherical harmonics, [Angular momentum] Motivation: angular momentum in the hydrogen atom, as derived from spherical harmonics, angular momentum in the abstract setting, intrinsic angular momentum, addition of angular momenta, Clebsch-Gordan coefficients, [Piecewise constant one-dimensional potentials] Bound and unbound states, wells and barriers, scattering, transmission coefficients, tunneling, [The harmonic oscillator] Creation and annihilation operators, coherent states, [Approximation methods] Time-independent perturbation theory: the non-degenerate case, variational methods for estimating the ground-state energy [Introduction to Quantum Information] Qubits and quantum logic gates

Further topics may include: Spin coherent states, how to build a microwave laser, the Dyson series for time-evolution for time-dependent Hamiltonians, one-dimensional Dirac potentials, time-independent perturbation theory for degenerate eigenstates, the fine structure of Hydrogen, numerical (spectral) methods for solving the Schrodinger equation

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*Curricular information is subject to change*

Learning Outcomes:

On completion of this module students should be able to

1. Perform standard linear-algebra calculations as they relate to the mathematical foundations of Quantum Mechanics;

2. Solve standard problems for systems with finite-dimensional Hilbert spaces, e.g. the two-level system

3. Solve standard one-dimensional models including the Harmonic oscillator;

4. Use of creation and annihilation operators, including the characterisation of coherent states;

5. Compute expectation values for appropriate observables for the Hydrogen atom;

6. Explain the quantum theory of angular momentum and compute expectation values for appropriate observables. These computations will involve both the matrix representation of intrinsic angular momentum, and the spherical-harmonic representation of orbital angular momentum;

7. Add independent angular momenta in the quantum-mechanical fashion;

8. Understand the foundations of quantum logic

Student Effort Hours:

Student Effort Type | Hours |
---|---|

Specified Learning Activities | 24 |

Autonomous Student Learning | 45 |

Lectures | 31 |

Total | 100 |

Approaches to Teaching and Learning:

Lectures and problem-based learning

Lectures and problem-based learning

Requirements, Exclusions and Recommendations

Students should have followed

ACM30010 Analytical Mechanics

or equivalent.

Module Requisites and Incompatibles

Not applicable to this module.
Assessment Strategy

Description | Timing | Component Scale | % of Final Grade | ||
---|---|---|---|---|---|

Examination: 2 hour End of Trimester Exam | 2 hour End of Trimester Exam | No | Standard conversion grade scale 40% | No | 60 |

Continuous Assessment: Take-home assignments and in-class exams | Varies over the Trimester | n/a | Standard conversion grade scale 40% | No | 40 |

Carry forward of passed components

No

No

Resit In | Terminal Exam |
---|---|

Autumn | Yes - 2 Hour |

Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Name | Role |
---|---|

Professor Adrian Ottewill | Lecturer / Co-Lecturer |

Dr Manya Sahni | Lecturer / Co-Lecturer |

Manya Sahni | Lecturer / Co-Lecturer |