Module Directory

Quantum Mechanics has been at the root of the enormous advances and major discoveries in Physics over the last century, having strong influence on the development of modern technology, like lasers, transistors and superconductors.

It gives a description of nature that is very different from the one of Classical Mechanics, in particular being non-deterministic and "non-local", and seeming to give a crucial role to the presence of "observers"

The aims of this module are:

• to provide students with a conceptual understanding of Quantum Mechanics, highlighting the break with "classical physics" concepts.


• to learn a fundamental theory describing the physical world through combining their mathematical skills learned in earlier stages. Through lectures, classes and seminars, students will develop graduate skills, like ability to assimilate, process and engage with new material quickly and efficiently.


• to develop problem-solving skills and learn how to apply learned techniques to unseen problems.

By the end of the module, students will be expected to be able to:

1. Demonstrate systematic understanding of the basic principles of quantum mechanics and be able to apply them in simple physical situations.


2. Solve simple eigenfunction problems for Hermitian operators.


3. Calculate the quantum mechanical wave function, probability distribution in a given state.


4. Calculate quantum mechanical expectation values of observables. Predict how the state of an undisturbed quantum system evolves with time.


5. Demonstrate the capability accurately to analyse and solve problems using a reasonable level of skill in in the following areas: potential wells and barriers in one dimension and the treatment of eigenvalue problems in quantum mechanics.


6. Apply key aspects of quantum mechanics in well-defined contexts, showing judgement in the selection and application of tools and techniques.


7. Gain knowledge and understanding of basic results about theory of linear operators in a Hilbert space.

The module begins with a brief historical and conceptual introduction, explaining the reasons for the failure of classical ideas, and the corresponding changes needed to describe the physical world. Then it presents the Schrodinger picture in Quantum mechanics.

Indicative syllabus

Early quantum physics: quanta and particles. Bohr model of the hydrogen atom.

De Broglie waves.

The Schrodinger equation and the wave function.

The time-independent Schrodinger equation: potential barriers and potential wells.

Formalism of quantum mechanics: states and observables. Postulates of Quantum mechanics. Dirac bra- and ket- vectors. Hilbert space (non-rigorous treatment).

Expectation values and commutation relations.

Quantum harmonic oscillators. Raising and lowering operators.

Time evolution in Quantum Mechanics. Symmetries and conserved quantities.

Schrodinger versus Heisenberg (interaction) picture.

Teaching in the School will be delivered using a range of face-to-face lectures, classes, and lab sessions as appropriate for each module. Modules may also include online only sessions where it is advantageous, for example for pedagogical reasons, to do so.