Physics and astronomy

Quantum Mechanics 1

Module code: F3239
Level 5
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
  • 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

Pre-requisite

Pre-requisites:
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.