A description of atomic and subatomic systems must be quantum mechanical in nature. This course explores the evidence for quantum bahaviour, introduces the postulates of quantum mechanics and develops the associated mathematical formalism. The course is designed to give a working knowledge of quantum mechanics and will be illustrated by examples from nuclear and atomic physics. Topics include; wave-particle duality; barrier penetration; wave-functions; Schrodinger Eqn; observables as operators, measurement, eigenvalues and collapse of the wave-function; Solution of the Schrodinger Eqn for Square Well and SHO; the Hydrogen Atom; Angular Momenta and Spin; Time evolution of Wave-functions; introduction to time (in)dependent perturbation theory.

Learning Outcomes

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

Understand wave-particle duality;

Be familiar with the histoical development of quantum mechanics;

Perform approximate calculations using the de Broglie relation and the Heisenberg 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 SchrÃ¶dinger equations;

Solve the time-independent SchrÃ¶dinger equation for simple 1-D and 3-D potential problems;

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

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

Describe the properties of angular momentum in quantum mechanics;

Relate the quantum numbers of atomic electrons or nucleons to physical variables and know how their different values are related;

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

Compute the time-dependence of expectation values;

Have an understanding of perturbation theory for time-independent, time-dependent problems.