Coherent states for continuous spectrum operators with non-normalizable fiducial states

Abstract

The problem of building coherent states from non-normalizable fiducial states is considered. We propose a way of constructing such coherent states by regularizing the divergence of the fiducial state norm. Then, we successfully apply the formalism to particular cases involving systems with a continuous spectrum: coherent states for the free particle and for the inverted oscillator $(p^2-x^2)$ are explicitly provided. Similar ideas can be used for other systems having non-normalizable fiducial states.

17 pages, typos corrected, references added

References in corpus (2)

• A theoretical scheme for generation of Gazeau-Klauder coherent states via intensity-dependent degenerate Raman interaction
• Nonclassical properties of coherent states and excited coherent states for continuous spectra

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