• To provide an introduction into basic concepts of quantum mechanics.
• To advance knowledge of quantitative analysis of molecular spectra.

(LO1) Demonstrate an understanding of the basic concepts of quantum mechanics, including operators and wavefunctions, and their application to simple systems.

(LO2) Show an understanding of different types of molecular energy levels, the forms of spectroscopy which involve transitions between them, and how molecular quantities can be extracted from the spectra.

(S1) Critical thinking and problem solving - Evaluation

(S2) Critical thinking and problem solving - Problem identification

(S3) Numeracy/computational skills - Reason with numbers/mathematical concepts

(S4) Numeracy/computational skills - Confidence/competence in measuring and using numbers

(S5) Numeracy/computational skills - Problem solving

Lectures: 18 lectures, to be complemented by one or more revision lectures at the end of term.

Workshops: The material presented at the lectures and its application for solving problems is supported by 4 x 2 hr workshops given over the semester.
Questions will cover fundamentals, background, practice and more advanced problems.

*Lectures: 18 hr
*Workshops: 8 hr

Quantum mechanics
1.Basic postulates of quantum mechanics and their interpretation, including: wave-functions and Born interpretation and Heisenberg uncertainty relations.
2.Methods of quantum mechanics including: properties of operators and the relationship to physical observables, eigenvalue equations and expectation values, transition dipole moments.
3.Hamiltonian and momentum operators, the basics of the Schrödinger equation.
4.Examples of the Schrödinger equation, including: particle in a one-dimensional box, particle on a ring, tunnelling, atomic and molecular energy levels, potential energy curves, the Born-Oppenheimer Approximation.
5.Bonding in simple molecules.

Spectroscopy
1.The basics of spectra formation: transitions, energy scales, line widths.
2.Rotation spectra of diatomics: eigenvalues, selection rules, line spacing, quantitative description.
3.Harmonic oscillator model of molecular vibrations: eigenvalues, selection rules.
4.The rotation-vibrations spectrum: qualitative appearance, line spacings in the harmonic oscillator rigid rotor approximation, quantitative description.
5.Anharmonicity: comparison to harmonic oscillator, effects on IR spectra.
6.Vibrations of polyatomics (revision).
7.Electronic transitions: the Franck-Condon Principle, selection rules, vertical transitions, vibrational structure.