Synopsis for Quantum Theory

Overview

Quantum theory was born out of the attempt to understand the interactions between radiation, described by Maxwell's theory of electromagnetism, and matter, described by Newton's mechanics.

Although there remain deep mathematical and physical questions at the frontiers of the subject, the resulting theory encompasses not just the mechanical but also the electrical and chemical properties of matter. Many of the key components of modern technology such as transistors and lasers were developed using quantum theory.

In quantum theory particles also have some wave-like properties. This introductory course explores some of the consequences of this culminating in an elementary treatment of the hydrogen atom.

Synopsis

Wave-particle duality; the Schrödinger equation; stationary states; quantum states of a particle in a box (infinite square-well potential)

Interpretation of the wave function; boundary conditions; probability density and conservation of current; degeneracy and parity.

The one-dimensional harmonic oscillator; higher-dimensional oscillators and normal modes.

The rotationally symmetric and general radial states of the hydrogen atom with fixed nucleus.

1. B. H. Bransden and C.J Joachain Quantum Mechanics (Second edition, Pearson Education Limited, 2000). Chapters 1-4.
   
2. P.C. W. Davies and D.S. Betts, Quantum Mechanics (Physics and its Applications) (2nd edition, Taylor & Francis Ltd, 1994). Chapters 1,2,4.
   
3. R.P Feynman, R.B Leighton, M. Sands The Feynman Lectures on Physics, Volume 3(Addison-Wesley, 1998). Chapters 1,2 (for physical background).
4. K.C Hannabuss, An Introduction to Quantum Theory (Oxford University Press 1997). Chapters 1-4.
5. A.I.M. Rae, Quantum Mechanics (4th Edition, Taylor & Francis Ltd, 2002). Chapters 1-3.