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The HVT Technique and the "Uncertainty" Relation for Central

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Published: Aug 30, 2021
DOI: https://doi.org/10.12681/hnps.3351
M. Grypeos
C. G. Koutroulos
K. J. Oyewumi
Th. Petridou
Abstract

The quantum mechanical hypervirial theorems (HVT) technique is used to treat the so-called "uncertainty" relation for quite a wide class of central potential wells, including the (reduced) Poeschl-Teller and the Gaussian one.
It is shown that this technique is quite suitable in deriving an approximate analytic expression in the form of a truncated power series expansion for the dimensionless product $P_{nl}\equiv <r^2>_{nl}<p^2>_{nl}/\hbar^2$, for every (deeply) bound state of a particle moving non-relativistically in the well, provided that a (dimensionless) parameter s is sufficiently small. Numerical results are also given and discussed.

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M.E. Grypeos, C.G. Koutroulos, K.J. Oyewumi, Th. Petridou, submitted for publication.