The HVT technique and the treatment of two basic inequalities

Grypeos, M. E.; Koutroulos, C. G.; Petridou, Th.

doi:10.1088/0305-4470/35/9/312

Cited by 3 publications

(2 citation statements)

References 22 publications

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“…We also note that this − s power series method was used in recent years in treating a variety of problems in which a small parameter s (see below) can be defined. We mention, in particular, the study of the saturation property of the Bertlmann and Martin [17,18] inequalities [19], the information on the size of − Λ orbitals in hypernuclei from the experimental − Λ energies [20], the approximate analytic evaluation of the Heisenberg uncertainty product [21] etc.…”

Section: Introductionmentioning

confidence: 99%

A new Λ- nucleus potential for the Λ- particle energies in hypernuclei

Efthimiou¹,

Grypeos²,

Koutroulos³

et al. 2020

hnps

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A new single particle Λ− nucleus potential is considered for the study of the Λ−particle energies in hypernuclei. This potential belongs to the class of potentials for which the formalism of the s−power series expansions of the Hypervirial Theorems technique is applicable. The numbers d_k (k = 0, 1, 2, 3, 4) related to the derivatives of the potential form factor f , determining the potential shape, are obtained and therefore the approximate analytic expression of the energy level Enl (including third-order terms in the small parameter s). Preliminary numerical results are also given and a discussion is made.

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Section: Introductionmentioning

confidence: 99%

A new Λ- nucleus potential for the Λ- particle energies in hypernuclei

Efthimiou¹,

Grypeos²,

Koutroulos³

et al. 2020

hnps

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“…Our method is based on the virial theorem applied to the harmonic oscillator and the hydrogen atom systems to obtain the uncertainty product, while for the spherical well, the zeros of spherical Bessel functions are used for finding numerical results for the uncertainty product. Over the last years, the virial theorem technique has been employed in the study of physical quantities [48] [49]. Interesting features for the lower bound are discussed with a special attention explored for the large space dimension limit for the spherical well system.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Relations for Some Central Potentials in N-Dimensional Space

Al-Jaber¹

2016

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We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the space dimension N. It is pointed out that the form of lower bound of the inequality, which is governed by the ground state, depends on the system and on the space dimension N. A comparison between our result for the lower bound and recent results, based on information-theoretic approach, is pointed out. We examine and analyze these derived uncertainties for different angular momenta with a special attention made for the large N limit.

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