# 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.