EIGENSTATES AND EIGENVALUES OF THE SU(1,1) DISPLACEMENT OPERATORS

Authors
LO CF WONG YJ
Citation
Cf. Lo et Yj. Wong, EIGENSTATES AND EIGENVALUES OF THE SU(1,1) DISPLACEMENT OPERATORS, Nuovo cimento della Societa italiana di fisica. B, Relativity, classical a, 113(1), 1998, pp. 125-129
Citations number
20
Categorie Soggetti
Physics
Journal title
Nuovo cimento della Societa italiana di fisica. B, Relativity, classical a
ISSN journal
11241888 → ACNP
Volume
113
Issue
1
Year of publication
1998
Pages
125 - 129
Database
ISI
SICI code
1124-1888(1998)113:1<125:EAEOTS>2.0.ZU;2-P
Abstract
In this paper we have constructed the continuum eigenfunctions and eig envalue spectrum of the SU(1, 1) Lie group displacement operator for t he positive discrete series representation in the Hilbert space of ana lytic functions in the unit disc, irrespective of the values of the Ba rgmann index. Our analysis also shows explicitly that proper (normaliz ed) eigenstates of the SU(1, 1) displacement operator do not exist, wh ich implies that the displacement operator does not have a discrete ei genvalue spectrum.