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Eigenstates of boson creation operator

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Abstract:

We examine the existence of right-hand eigenstates (or eigenkets) of the boson creation operator a 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.

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Authors and Affiliations

  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, , , , , , CN

    H.-y. Fan

  2. Institut für Physik, Humboldt-Universität, Invalidenstr. 110, 10115 Berlin, Germany, , , , , , DE

    A. Wünsche

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  1. H.-y. Fan
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  2. A. Wünsche
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Received 9 March 2001 and Received in final form 13 June 2001

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Fan, Hy., Wünsche, A. Eigenstates of boson creation operator. Eur. Phys. J. D 15, 405–412 (2001). https://doi.org/10.1007/s100530170157

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  • DOI: https://doi.org/10.1007/s100530170157

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