https://doi.org/10.1140/epjp/s13360-023-04164-1
Regular Article
Higher-order phase-space moments for Morse oscillators and their harmonic limit
1
PTEA Laboratory, Physics Department, Faculty of Sciences, Yahia FARES University, 26000, Médéa, Algeria
2
LPTHIRM, Département de physique, Faculté des sciences, Université Saâd DAHLAB-Blida 1, B.P. 270, Route de Soumâa, 09000, Blida, Algeria
Received:
12
March
2023
Accepted:
1
June
2023
Published online:
16
June
2023
An explicit and general formula for (m, l) diagonal higher-order phase-space moments (i.e. matrix elements) 
for the Morse oscillator potential is presented. We show that this formula is more extended than those currently available in the literature and can be carried out using a phase-space Wigner distribution function in conjunction with its characteristic function. In the case it is wanted, the obtained formula gives the explicit form of the expected values of position and momentum in terms of the potential parameters. The validity of these expressions is tested by giving a numerical comparison with those obtained by other approximations. Moreover, it makes it possible to approach straightforwardly the harmonic limit of the Morse oscillator potential using the Heisenberg uncertainty product. We show indeed that when changing the potential depth, a common pattern emerges as a linear behavior on n in the form 
, applied to all levels 
, indicating the signature of the so-called harmonic limit of the Morse oscillator potential.
This paper is dedicated to the memory of Professor Mustapha Bentaiba, beloved friend and esteemed colleague and teacher, who passed away on December 3rd, 2018.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
