The discrete canonical commutation relationship

We use non-standard finite differences to propose a quantum momentum operator to be used when the spectrum of the operator is discrete. The defined discrete operator complies with the discrete versions of the properties that the continuous variable operator has. The discrete derivative is exact for...

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Bibliographic Details
Published in:Physica scripta 2023-11, Vol.98 (11), p.115254
Main Authors: Martínez-Pérez, Armando, Torres-Vega, Gabino
Format: Article
Language:English
Subjects:
discrete commutator
discrete quantum mechanics
discrete quantum momentum operator
exact finite-differences derivative
quantum canonical commutator
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Summary:We use non-standard finite differences to propose a quantum momentum operator to be used when the spectrum of the operator is discrete. The defined discrete operator complies with the discrete versions of the properties that the continuous variable operator has. The discrete derivative is exact for its eigenfunction, that is, exponential functions. We obtain the discrete adjoint of the momentum operator. The canonical commutation relationship between conjugate operators for discrete variables is diagonal along a particular direction.
ISSN:0031-8949
1402-4896
DOI:10.1088/1402-4896/ad00e0