¹û¶³Ó°Ôº

Outline:

This is an introductory module in quantum mechanics covering the failure of classical Newtonian mechanics and the basics of quantum mechanics motivated by physical examples. It aims to develop an understanding of the principles of Quantum Mechanics and their implications to the solution of physical problems. It forms the essential basis for many of the succeeding modules within Physics and Astronomy.

Aims:

To provide an introduction to the basic ideas of non-relativistic quantum mechanics and to introduce the methods used in the solutions of simple quantum mechanical problems. This module prepares students for further study of atomic physics, quantum physics, and spectroscopy. It is a prerequisite for PHAS0023 Atomic and Molecular Physics, PHAS0042 Quantum Mechanics, PHAS0018 Astrophysical Processes and PHAS0047 Astronomical Spectroscopy.

Intended Learning Outcomes:

By the end of this module students should:

• be able to solve one-dimensional problems in non-relativistic quantum mechanics
• be familiar with the quantum treatment of angular momentum and be able to perform calculations with it.
• to solve the Schrodinger equation for the hydrogen atom.Ìý
• be familiar with the underlying postulates of quantum mechanics and their mathematical formulation.Ìý
• posses an introductory understanding of the notion of spin and the experimental motivation for it.Ìý

Teaching and Learning Methodology:

This module is delivered via weekly lectures supplemented by a series of problem solving tutorials and additional discussion.

In addition to timetabled lecture and PST hours, it is expected that students engage in self-study in order to master the material. This can take the form, for example, of practicing example questions and further reading in textbooks and online.

Indicative Topics:

• The failure of classical mechanics. Revision of key concepts and seminal experiments: photoelectric effect, Einstein’s equation, Compton scattering, electron diffraction and de Broglie relation
• Steps towards wave mechanics. Wave-particle duality, Uncertainty principle (Bohr microscope); Time-dependent and time-independent Schrödinger equations; The wave function and its interpretation
• One-dimensional time-independent problems. Infinite square well potential; Finite square well; Probability flux and the potential barrier and step; Reflection and transmission; Tunnelling and examples in physics and astronomy; Wavepackets; The simple harmonic oscillator
• The formal basis of quantum mechanics. The postulates of quantum mechanics – operators, observables, eigenvalues and eigenfunctions; Hermitian operators and the Expansion Postulate
• Angular momentum in quantum mechanics. Operators, eigenvalues and eigenfunctions of Lz and L2.
• Three dimensional problems and the hydrogen atom. Separation of variables for a three-dimensional rectangular well; Separation of space and time parts of the 3D Schrödinger equation for a central field; The radial Schrödinger equation, and casting it in a form suitable for solution by series method; Degeneracy and spectroscopic notation
• Periodic potentials and crystals. Kronig Penney model; Free electron model; Band structure
• Electron spin and total angular momentum. Magnetic moment of electron due to orbital motion; The Stern-Gerlach experiment; Electron spin and complete set of quantum numbers for the hydrogen atom; Rules for addition of angular momentum quantum numbers; Total spin and orbital angular momentum quantum numbers S, L, J; Construct J from S and L.Ìý