Bi-coherent states as generalized eigenstates of the position and the momentum operators

• URL: http://arxiv.org/abs/2204.09044v2
• Date: Tue, 17 May 2022 10:22:15 GMT
• Title: Bi-coherent states as generalized eigenstates of the position and the momentum operators
• Authors: Fabio Bagarello, Francesco Gargano
• Abstract summary: We show that the position and the derivative operators, $hat q$ and $hat D$, can be treated as ladder operators connecting two biorthonormal families. We show how bi-coherent states can be constructed for these $hat q$ and $hat D$, both as convergent series of elements of $mathcalF_varphi$ and $mathcalF_psi$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In this paper we show that the position and the derivative operators, $\hat q$ and $\hat D$, can be treated as ladder operators connecting the various vectors of two biorthonormal families, $\mathcal{F}_\varphi$ and $\mathcal{F}_\psi$. In particular, the vectors in $\mathcal{F}_\varphi$ are essentially monomials in $x$, $x^k$, while those in $\mathcal{F}_\psi$ are weak derivatives of the Dirac delta distribution, $\delta^{(m)}(x)$, times some normalization factor. We also show how bi-coherent states can be constructed for these $\hat q$ and $\hat D$, both as convergent series of elements of $\mathcal{F}_\varphi$ and $\mathcal{F}_\psi$, or using two different displacement-like operators acting on the two vacua of the framework. Our approach generalizes well known results for ordinary coherent states.

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