Module Identifier PH23720  
Module Title QUANTUM MECHANICS 1  
Academic Year 2006/2007  
Co-ordinator Dr Rudolf Winter  
Semester Semester 2  
Other staff Mr Daniel Le Messurier  
Pre-Requisite Core physics modules at level 1  
Course delivery Lecture   40 x 1 hr lectures  
  Seminars / Tutorials   2 tutorials  
  Workload Breakdown   (Every 10 credits carries a notional student workload of 100 hours) Lectures 40 hrs Example sheets 20 hrs Tutorials 2 hrs Private study 138hrs  
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam3 Hours Written examination  70%
Semester Assessment 2 example sheets30%
Supplementary Exam3 Hours Written examination  100%

Learning outcomes

On successful completion of this module students should be able to:
1. Describe the basic principles of the quantum mechanical concepts of waves, particles and wave packets.

2. Explain the limits of classical physics at the microscopic level and formulate basic physical systems in terms of Schrodinger's equation

3. Identify the concepts that lead to the explanation of discrete bound states, scattering and tunneling on the smallest scales, including the fundamental ideas behind the quantum solution of the hydrogen atom.

4. Appreciate the concept of spin in understanding magnetic properties of materials.

5. Solve simple numerical problems in quantum mechanics at the microscopic level.

Aims

Quantum mechanics is a theory developed to explain inconsistencies of classical mechanics when dealing with very small objects. Its fundamental idea is that energy is not a continuous quantity but comes in small packets ("quanta") of uniform size. Classical mechanics is fully contained in quantum mechanics as its limit for objects of larger than atomic size. However, quantum mechanics has implications for phenomena at much larger scales, e.g. energy bands in solids. Quantum-mechanical properties are the basis of techniques such as magnetic resonance imaging and scanning tunnelling microscopy.

Brief description

Building on the Year 1 models "The Quantum Universe" this Year 2 20 credit module develops the Quantum Physics of the microscopic world.The mathematical equivalence and physical distinction between the Wave Equation and Schrondinger'r Equation are emphasised at the macroscopic and quantum level. Photons, electrons and neutrons are described and the consequences of the Uncertainty Principle emphasised. Quantisation, scattering and tunneling phenomena are covered in the context of the particle in a well and the simple harmonic oscillator. The quantum solution of the hydrogen atom is given and the concept of spin is extended to the understanding of magnetic properties. Throughout the module illustrative numerical problems are given relating to quantum mechanics and wave-particles

Content

Limits of classical mechanics
Recap of wave-particle duality.
De Broglie relationships and Schrodinger's equation.
Operators, dynamical variables and possible results of a measurement. Expectation values.
Solution of Schrodinger's equation for an infinite well.
Degeneracy. Correspondence Principle. Symmetric and anti-symmetric solution.
Zero-point energy and specific heat at low temperatures. Uncertainty Principle.
Potential well with ion lattice. Symmetry argument for valence and conduction bands. Insulators, conductors and semi-conductors.
Bosons and Fermions. Atoms, molecules and solids
Scattering by a finite well and Ramsauer effect.
Barrier penetration (approximate solution). Field-emission microscope and scanning microscope.
Quantum representation of angular momentum.
Hydrogen atom.
Spin, directional quantisation magnetism and NMR.
Quantum entanglement.

Module Skills

Problem_solving Students are required to apply theoretical concepts covered in lectures to specific science problems.  
Improving own Learning and Performance Feedback from example sheets will help students improve learning  
Application of Number Physics problems are heavily numeracy-dependent  

Reading Lists

Books
** Recommended Text
French, A.P. & Taylor, E. F. (2003) An Introduction to Quantum Physics Chapman and Hall 041237580X
Hey, Anthony J. G. (2003.) The new quantum universe /Tony Hey, Patrick Walters. http://www.loc.gov/catdir/toc/cam031/2002074047.html 0521564573
House, J. E. (c1998.) Fundamentals of quantum mechanics /J.E. House. 0123567750

Notes

This module is at CQFW Level 5