Quantum Mechanics 1 (F3239)

15 credits, Level 5

Spring teaching

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
  • derivative.
  • 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

Teaching and assessment

We’re currently reviewing teaching and assessment of our modules in light of the COVID-19 situation. We’ll publish the latest information as soon as possible.

Contact hours and workload

This module is approximately 160 hours of work. This breaks down into about 43 hours of contact time and about 117 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.

This module is running in the academic year 2020/21. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.

Courses

This module is offered on the following courses: