Abstract ladder operators and their applications

• URL: http://arxiv.org/abs/2109.10171v1
• Date: Tue, 21 Sep 2021 13:38:49 GMT
• Title: Abstract ladder operators and their applications
• Authors: Fabio Bagarello
• Abstract summary: We consider a general version of ladder operator $Z$ used by some authors in few recent papers. We extend it in two ways: first we replace the original equality with formula $[H,Z]=lambda Z[Zdagger, Z]$, and secondly we consider $[H,Z]=lambda Z$ for some $lambdainmathbbC$, $Hneq Hdagger$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a rather general version of ladder operator $Z$ used by some authors in few recent papers, $[H_0,Z]=\lambda Z$ for some $\lambda\in\mathbb{R}$, $H_0=H_0^\dagger$, and we show that several interesting results can be deduced from this formula. Then we extend it in two ways: first we replace the original equality with formula $[H_0,Z]=\lambda Z[Z^\dagger, Z]$, and secondly we consider $[H,Z]=\lambda Z$ for some $\lambda\in\mathbb{C}$, $H\neq H^\dagger$. In both cases many applications are discussed. In particular we consider factorizable Hamiltonians and Hamiltonians written in terms of operators satisfying the generalized Heisenberg algebra or the $\D$ pseudo-bosonic commutation relations.

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