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, Fφ and Fψ. In particular, the vectors in Fφ are essentially monomials in x, xk, while those in Fψ 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 Fφ and Fψ, 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.

Bagarello F., Gargano F. (2022). Bi-coherent states as generalized eigenstates of the position and the momentum operators. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 73(3) [10.1007/s00033-022-01759-z].

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

Bagarello F.;Gargano F.
2022-06

Abstract

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, Fφ and Fψ. In particular, the vectors in Fφ are essentially monomials in x, xk, while those in Fψ 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 Fφ and Fψ, 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.
Settore MAT/07 - Fisica Matematica
https://link.springer.com/article/10.1007/s00033-022-01759-z
Bagarello F., Gargano F. (2022). Bi-coherent states as generalized eigenstates of the position and the momentum operators. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 73(3) [10.1007/s00033-022-01759-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/564825
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