We consider a rather general version of ladder operator Z used by some authors in few recent papers, [H 0, Z] = λZ for some, H0=H0†, 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] = λZ[Z †, Z], and secondly we consider [H, Z] = λZ for some C, H ≠ H †. 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.

Bagarello F. (2021). Abstract ladder operators and their applications. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 54(44), 445203 [10.1088/1751-8121/ac28cf].

Abstract ladder operators and their applications

Bagarello F.
2021-01-01

Abstract

We consider a rather general version of ladder operator Z used by some authors in few recent papers, [H 0, Z] = λZ for some, H0=H0†, 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] = λZ[Z †, Z], and secondly we consider [H, Z] = λZ for some C, H ≠ H †. 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.
2021
Settore MAT/07 - Fisica Matematica
Bagarello F. (2021). Abstract ladder operators and their applications. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 54(44), 445203 [10.1088/1751-8121/ac28cf].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/528546
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