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Bagarello, F.; Gargano, F.
Zeitschrift für angewandte Mathematik und Physik, 06/2022, Volume: 73, Issue: 3Journal Article
In this paper, we show that the position and the derivative operators, q ^ and D ^ , can be treated as ladder operators connecting various vectors of two biorthonormal families, F φ and F ψ . In particular, the vectors in F φ are essentially monomials in x , x k , while those in F ψ are weak derivatives of the Dirac delta distribution, δ ( m ) ( x ) , times some normalization factor. We also show how bi-coherent states can be constructed for these q ^ and D ^ , both as convergent series of elements of F φ and F ψ , 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.
