Representations of Coherent States in Non-orthogonal Bases

Details Representations of Coherent States in Non-orthogonal Bases Representations of Coherent States in Non-orthogonal Bases

2003-10-23

arxiv.org/abs/quant-ph/0310147v1

Physics

Quantum Physics

Scientific paper

10.1088/0305-4470/37/15/009

Starting with the canonical coherent states, we demonstrate that all the so-called nonlinear coherent states, used in the physical literature, as well as large classes of other generalized coherent states, can be obtained by changes of bases in the underlying Hilbert space. This observation leads to an interesting duality between pairs of generalized coherent states, bringing into play a Gelfand triple of (rigged) Hilbert spaces. Moreover, it is shown that in each dual pair of families of nonlinear coherent states, at least one family is related to a (generally) non-unitary projective representation of the Weyl-Heisenberg group, which can then be thought of as characterizing the dual pair.

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