Module description
Learning aims & outcomes
This introductory course aims to give students a solid grounding in modern quantum theory.
- Students will gain the skills to understand and apply basic quantum mechanics
This will involve being able to confidently solve the Schroedinger equation in a variety of physical situations, and calculate measurement probabilities. You will learn the language of quantum mechanics, namely Dirac notation and the use of matrices. You will learn the basics of quantum angular momentum and spin. The course will be summarized in a skills-based lecture.
- Students will gain the confidence to tackle a wide range of scientific problems
This will be achieved through the use of various techniques to apply the skills you have learned. In the lecture course, your learning will be consolidated and applied to understanding the Hydrogen atom. Problem classes will allow you to apply your skills to a wide and deep range of tasks. You will be introduced to modern techniques through programming tasks, including a 4-hour long session on visualization.
Syllabus
- The concept of a photon, and evidence for it.
- Bohr model of the atom, and evidence for it.
- The concept of matterwaves, calculation of the de Broglie wavelength, and interpretation of the result.
- Separation of variables and the derivation of the time-independent Schroedinger equation.
- Using the Schroedinger equation to calculate the energies of a particle in an infinite square well.
- Familiarity with the techniques to solve the finite square well and harmonic potential problems.
- Calculation of quantum tunnelling fractions.
- How to calculate probability from a wavefunction.
- How to calculate averages / expectation values using a wavefunction.
- Wavefunction expansion, its interpretation, and calculation of expansion coefficients.
- The meaning of eigenfunctions, eigenvalues, operators and observables, and their manipulation.
- Raising and lowering operators for the harmonic oscillator.
- Vector representation of wavefunctions.
- Matrix representation of operators.
- Dirac notation and manipulation of bra-kets.
- Hermitian operators: what they represent and how to prove an operator is Hermitian.
- Commutation relations and their physical interpretation.
- Familiarity with angular momentum commutation relations.
- The z-component-of-angular-momentum operator and its interpretation. The derivation of its eigenfunctions and eigenvalues.
- The angular-momentum-squared operator and its interpretation. Spherical harmonics as its eigenfunctions, the relation between its eigenvalues and the eigenvalues of the z-component.
- Familiarity with the derivation of the Radial Equation.
- The physical interpretation of spin and the Stern-Gerlach experiment.
- Dirac notation representation of spin.
- The matrix representation of spin (spinors), its operators and its eigenvalues.
- The operator for spin in an arbitrary direction.
- Measurement, repeated measurement, probability and expectation values of spin.
- Transitions between energy levels in the Hydrogen atom.
- Familiarity with the Schroedinger equation for Hydrogen, and the effective potential.
- Familiarity with the technique to solve the Radial equation for Hydrogen.
- Interpretation of the radial wavefunctions.
- Calculating probability using the radial wavefunctions.
Assessment details
Details of the module's assessment/s
| Type |
Weighting |
Marking model |
Written two hour exam (May)
Quizzes
Matlab Task
Research Report |
70%
10%
10%
10% |
Model 2. Double Marking
|
Teaching pattern
Asynchronous recorded lectures (1 hour per week)
Synchronous flipped classroom (1-2 hour per week)