2012/10/19 by C V Sukumar, Sukumar, C. V.
Chemistry · Computer Science · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.1210.5331
openalex publication_date 2012/10/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
It is shown that a SU(1,1) algebra may be used to provide a unified description of the simple hamonic oscillator and the angular momentum algebras and a class of other semi-infinite algebras. A normal ordered representation of a Unitary operator U constructed from the generators of a SU(1,1) algebra, which is a generalisation of the Baker- Campbell - Hausdorff relation for Lie algebras, is given. It is shown that the normal ordered representatiion of U may be used to calculate expectation values which are functions of the parameters used to construct the operator. The functions so constructed satisfy certain recurrence relations and the entire set of functions may be interpreted in terms of diagrams similar to the Pascal triangle for binomial coefficients. Coherent states, squeezed states and rotation matrices of the angular momentum algebra emerge as special cases.