Physics and astronomy
Quantum Mechanics 1
Module code: F3239
15 credits in spring teaching
Teaching method: Lecture, Workshop
Assessment modes: Unseen examination, Coursework
Module topics include
- Introduction to quantum mechanics, wave functions and the Schroedinger equation in 1D.
- Statistical interpretation of quantum mechanics, probability density, expectation values, normalisation of the wave function.
- Position and momentum, Heisenberg uncertainty relation.
- Time-independent Schroedinger equation, stationary states, eigenstates and eigenvalues.
- Bound states in a potential, infinite square well.
- Completeness and orthogonality of eigenstates.
- Free particle, probability current, wave packets, group and phase velocities, dispersion.
- General potentials, bound and continuum states, continuity of the wave function and its first
- Bound states in a finite square well.
- Left- and right-incident scattering of a finite square well, reflection and transmission probabilities.
- Reflection and transmission at a finite square well.
- Reflection and transmission at a square barrier, over-the-barrier reflection, tunnelling, resonant
- tunnelling through multiple barriers.
- Harmonic oscillator (analytic approach).
- Quantum mechanics in 3D, degeneracy in the 3D isotropic harmonic oscillator.
- Orbital angular momentum, commutators and simultaneous measurement.
- Motion in a central potential, Schroedinger equation in spherical polar coordinates.
- Schroedinger equation in a Coulomb potential.
- H atom.
- Spin, identical particles, spin-statistics theorem.
- Helium, basics of atomic structure.
- Time-independent perturbation theory for non-degenerate bound states.
- Applications of perturbation theory, fine structure in the H atom.
- Schroedinger equation for a particle coupled to an electromagnetic field.
- Summary and revision
Level 4: (F3210) Classical Mechanics [T1].
Level 5: (F3204) Electrodynamics [T1]
Level 5: (F3205) Maths Methods 3 [T1]
Module learning outcomes
- A successful student should be able to: demonstrate an understanding of the basic characteristics of quantum systems.
- Demonstrate an understanding of the nature of the quantum mechanical wave function and its basic properties.
- Apply the stationary Schroedinger equation to simple quantum mechanical systems.
- Apply differential and integral calculus to determine basic properties of quantum mechanics systems.