Quantum monodromy and molecular spectroscopy
Monodromy (or once round) is a classical property of integrable dynamical systems in two or more degrees of freedom, which imposes a characteristic pattern on the quantum mechanical eigenvalue distribution. This article explains the connection by showing how the presence of an isolated
critical point of the Hamiltonian leads to a classical action function that is multi-valued with respect to energy and angular momentum. Consequently, by the Bohr correspondence principle between actions and quantum numbers, there can be no uniquely defined global system of quantum numbers.
Implications for the interpretation of highly excited molecular spectra are brought out by reference to quasi-linear molecules, which transfer one degree of freedom from rotational to vibrational motion during the excitation process. Emphasis is placed on the simplest examples, while a brief
resumé of the wide scope of the quantum monodromy phenomenon is given in the final section.
Keywords: angle-action; angular momentum; classical trajectory; energy; monodromy; quasi-linear molecules
Document Type: Research Article
Affiliations: Chemistry Department, Oxford University, Oxford, UK.
Publication date: 03 July 2014
- Editorial Board
- Information for Authors
- Subscribe to this Title
- Ingenta Connect is not responsible for the content or availability of external websites
- Access Key
- Free content
- Partial Free content
- New content
- Open access content
- Partial Open access content
- Subscribed content
- Partial Subscribed content
- Free trial content