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Quantum Theory and Spectroscopy

Prof. Dónall Mac Dónaill

Introduction to Quantum Theory and Spectroscopy

This course is designed to introduce the student to the fundamental aspects of quantum mechanics, quantum chemistry and its connection to electronic, vibrational and rotational spectroscopy.

The content is organised in 9 lectures covering the following topics:

Wave-particle duality and de Broglie’s relationship. Wave functions; complex waves. Heisenberg’s uncertainty principle. Schrodinger’s equations. Hamiltonian, momentum and position operators. Probability densities and normalisation. The postulates of Quantum Mechanics.

Wave function of a free particle. Particle in a box: level quantization, zero-point energy and symmetry. Particle in a well of finite depth. Tunnelling. Spectroscopic application of particle in a box: quantum dots and conjugated dyes.

The harmonic oscillator: eigenvalues and eigenfunctions, zero-point energy and symmetry. Spectroscopic applications of the harmonic oscillator model. Transitions between levels; molecular vibrations.

Particle in a ring. Angular momentum. The rigid rotor; level quantization. Spherical harmonics. Molecular rotations: rotational spectroscopy.

The hydrogen atom and atomic orbitals. Atomic transitions and atomic lines.

Lecture notes and problems are available on WebCT (code = CH2002b).

Recommended reading for the course:

- The Feynman Lectures on Physics Vol III, by Feynman, Leighton and Sands. Published by Addison-Wesley Publishing Company.

- Physics, by Halliday & Resnick. Published by Wiley&Sons.

- Physical Chemistry, by Atkins. Published by Freeman.

- The Elements of Physical Chemistry, by Atkins. Published by Oxford University Press.

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