scholarly journals The HVT Technique and the "Uncertainty" Relation for Central

2021 ◽  
Vol 12 ◽  
pp. 118
Author(s):  
M. Grypeos ◽  
C. G. Koutroulos ◽  
K. J. Oyewumi ◽  
Th. Petridou
Keyword(s):  
Power Series ◽  
Dimensionless Parameter ◽  
Uncertainty Relation ◽  
Power Series Expansion ◽  
Bound State ◽  
Quantum Mechanical ◽  
Potential Wells ◽  
Central Potential ◽  
Approximate Analytic Expression ◽  
Analytic Expression

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.

A RENORMALIZED HVT APPROACH AND ENERGIES OF A Λ-PARTICLE IN HYPERNUCLEI

2011 ◽  
Vol 20 (06) ◽  
pp. 1391-1407
Author(s):  
C. A. EFTHIMIOU ◽  
M. E. GRYPEOS ◽  
C. G. KOUTROULOS ◽  
K. J. OYEWUMI ◽  
TH. PETRIDOU
Keyword(s):  
Power Series ◽  
Wide Class ◽  
Quantum Mechanical ◽  
Series Expansions ◽  
Potential Well ◽  
Potential Wells ◽  
Central Potential ◽  
Energy Eigenvalues ◽  
Power Series Expansions

An investigation is carried out to consider a renormalized quantum mechanical HVT approach in the context of s-power series expansions for the Schrödinger energy eigenvalues of a particle moving in a central potential well belonging to a fairly wide class of potential wells. This approach is designed and applied in detail to estimate energies of a Λ in hypernuclei. The determination of the renormalization parameter is also discussed.

THE CURRENT CHARACTERISTICS OF TWO-STATE FLASHING RATCHETS COMPOSED OF TWO ASYMMETRIC POTENTIALS

2008 ◽  
Vol 22 (30) ◽  
pp. 2967-2978 ◽  
Author(s):  
TIANFU GAO ◽  
YUE ZHANG ◽  
JINCAN CHEN
Keyword(s):  
Power Series ◽  
Power Series Expansion ◽  
Expansion Method ◽  
Transition Rates ◽  
Probability Current ◽  
Brownian Particles ◽  
Analytic Expression ◽  
Current Characteristics ◽  
Flashing Ratchets ◽  
Series Expansion Method

The transport of Brownian particles in two-state flashing ratchets composed of two asymmetric potentials with the same period is investigated. The analytic expression of a probability current is derived by using the power series expansion method and used to generate the curve characteristics of the current varying with other parameters. The effects of the asymmetric parameters and heights of two potentials and the transition rates between two states on the probability current are discussed in detail. The influence of other parameters on the behaviors of the current is also analyzed. It is found that the current is affected by not only the asymmetric parameters and heights of two potentials but also the transition rates between two states. It is also found that the heights of two potentials may change the magnitude as well as the direction of the current when the transition rates between two states are not the same. It is expected that the results obtained here may be observed in some physical and biological systems.

scholarly journals A renormalized HVT approach for a class of central potential wells

2020 ◽  
Vol 16 ◽  
pp. 107
Author(s):  
C. A. Efthimiou ◽  
M. E. Grypeos ◽  
C, G. Koutroulos ◽  
W. J. Oyewumi ◽  
Th. Petridou
Keyword(s):  
Power Series ◽  
Recurrence Relations ◽  
Dimensionless Quantity ◽  
Third Order ◽  
Class V ◽  
Potential Wells ◽  
Central Potential ◽  
Energy Eigenvalues ◽  
State Dependent ◽  
Power Series Expansions

An investigation is carried out to consider a renormalized HVT approach in the context of s-power series expansions for the energy eigenvalues of a particle moving non-relativistically in a central potential well belonging to the class V(r)=−Df(rR), D>0 where f is an appropriate even function of x=r/R and the dimensionless quantity s = (h^2/2μDR)^{1/2} is assumed to be sufficiently small. Previously, the more general class of central potentials of even power series in r is considered and the renormalized recurrence relations from which the expansions of the energy eigenvalues follow, are derived. The s-power series of the renormalized expansion are then given for the initial class of potentials up to third order in s (included) for each energy-level Enl . It is shown that the renormalization parameter Κ enters the coefficients of the renormalized expansion through the state-dependent quantity a_{nl}χ^{1/2} =a_{nl}(1+K ((−d_1D)R^2))^{½}, a_{nl}=(2n+l+32). The question of determining χ is discussed. Our first numerical results are also given and the utility of potentials of the class considered (to which belong the well-known Gaussian and reduced Poschl- Teller potentials) in the study of single–particle states of a Λ in hypernuclei is pointed out.

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