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Quantum Algorithms
Abstract ladder operators and their applications
arXiv
Authors: Fabio Bagarello
Year
2021
Paper ID
61387
Status
Preprint
Abstract Read
~2 min
Abstract Words
110
Citations
N/A
Abstract
We consider a rather general version of ladder operator Z used by some authors in few recent papers, \[H0,Z\]=λZ for some λinmathbb{R}, H0=H0dagger, 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 \[H0,Z\]=λZ\[Zdagger, Z\], and secondly we consider [H,Z]=λZ for some λinmathbb{C}, Hneq Hdagger. 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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- It adds a 2021 reference point for readers tracking recent quantum research.
- We consider a rather general version of ladder operator Z used by some authors in few recent papers, [H0,Z]=λZ for some λinmathbbR, H0=H0^dagger, and we show that several...
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