Quantum Mechanics describes the behaviour of matter on sub-microscopic scales, and together with Relativity, is one of the two foundations of "modern" physics. Quantum systems are often described as having both "wave-like" and "particle-like" aspects to their behaviour, and are famous for producing results which defy "common sense" intuition based on observations at everyday scales. We will discuss the Schrodinger Equation and some of its applications as well as the concept of a wavefunction. We will illustrate some of the "non-intuitive" behaviour of quantum systems, show how it arises, and how in the limit of large energies, it tends towards classical behaviour. We will discuss "operators", the Uncertainty Principle and will introduce the quantum treatment of angular momentum as well as electron spin. We will consider how to write a wavefunction describing a pair of electrons, and show how the existence of complex chemistry, and thus of life, depends on the answer. And we'll also discuss what Schrodinger really meant with that business about the cat...

Learning Outcomes

By the end of the module students should be able to:

Perform approximate calculations using the de Broglie relation and the Heisenburg Uncertainty Principle

Normalise a wavefunction

Use wavefunctions to calculate expectation values and the probabilities of different outcomes of measurements

Show how measurement changes the wavefunction

Be familiar with the use of Hermitian operators to represent physical quantities in quantum mechanics and the properties of their eigenvalues and eigenfunctions

Explain the physical significance of each element of an eigenvalue equation

Be familiar with the time-dependent and time-independent Schrodinger equations

Solve the time-independent Schrodinger equation for simple 1-D and 2-D potential problems

Describe the main features of the solutions for a range of problems

Evaluate the commutator of two operators and explain its physical significance

Be aware of how the Pauli exclusion principle arises and be able to apply it to multi-electron systems

Describe the properties of angular momentum in quantum mechanics

Relate the quantum number of atomic electrons to physical variables and know how their different values are related

Explain why the concept of electron spin is required to explain experimental observations