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A direct proof of completeness of squeezed odd-number states

Quantum Physics 2008-11-26 v1

Abstract

A direct proof of the resolution of the identity in the odd sector of the Fock space in terms of squeezed number states D(ξ)2m+1>;D(ξ)=exp((ξa2ξa2)/2)D(\xi)|2m+1>; D(\xi) = \exp(({\xi}a^{\dagger2}-{\xi}^*{a^2})/2) is given. The proof entails evaluation of an integral involving Jacobi polynomials. This is achieved by the use of Racah identities.

Keywords

Cite

@article{arxiv.quant-ph/9608036,
  title  = {A direct proof of completeness of squeezed odd-number states},
  author = {S. Chaturvedi},
  journal= {arXiv preprint arXiv:quant-ph/9608036},
  year   = {2008}
}

Comments

6 pages, latex, no figures