56 research outputs found
Ladder operators for isospectral oscillators
We present, for the isospectral family of oscillator Hamiltonians, a
systematic procedure for constructing raising and lowering operators satisfying
any prescribed `distorted' Heisenberg algebra (including the
-generalization). This is done by means of an operator transformation
implemented by a shift operator. The latter is obtained by solving an
appropriate partial isometry condition in the Hilbert space. Formal
representations of the non-local operators concerned are given in terms of
pseudo-differential operators. Using the new annihilation operators, new
classes of coherent states are constructed for isospectral oscillator
Hamiltonians. The corresponding Fock-Bargmann representations are also
considered, with specific reference to the order of the entire function family
in each case.Comment: 13 page
Wave packet dynamics of the matter wave field of a Bose-Einstein condensate
We show in the framework of a tractable model that revivals and fractional
revivals of wave packets afford clear signatures of the extent of departure
from coherence and from Poisson statistics of the matter wave field in a
Bose-Einstein condensate, or of a suitably chosen initial state of the
radiation field propagating in a Kerr-like medium.Comment: 10 pages, 4 figures, RevTeX
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