https://doi.org/10.1007/s100530170157
Eigenstates of boson creation operator
1
Department of Applied Physics, Shanghai Jiao Tong
University, Shanghai 200030, P.R. China
and
Department of Material Science and Engineering, University of Science
and Technology of China, Hefei 230026, P.R. China
2
Institut für Physik, Humboldt-Universität,
Invalidenstr. 110, 10115 Berlin, Germany
Corresponding authors: a fhym@ustc.edu.cn - b alfred.wuensche@physik.hu-berlin.de
Received:
9
March
2001
Revised:
13
June
2001
Published online: 15 September 2001
We examine the existence of right-hand eigenstates (or eigenkets) of the boson
creation operator 
and determine their coordinate and their Bargmann
representation. The eigenkets of the creation operator are ultrasingular and
cannot be considered as a limiting case of normalizable states. Applications of
these eigenstates as auxiliary states for purposes of representation of states
by path integrals over coherent states are discussed. A completeness relation for
coherent states on paths through the complex plane is derived and special examples
of its application are considered.
PACS: 42.50.Dv – Nonclassical field states; squeezed, antibunched, and sub-Poissonian states; operational definitions of the phase of the field; phase measurements
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
