scholarly journals Application of the hypervirial theorem scheme to the potential -D/cosh^2(r/R)

2020 ◽  
Vol 4 ◽  
pp. 51
Author(s):  
T. Liolios ◽  
M. Grypeos
Keyword(s):  
Excited States ◽  
Energy Eigenvalues ◽  
Analytic Expressions ◽  
Hypervirial Theorem ◽  
Feynman Theorem

The well known potential -D/cosh^2(r/R)is studied with the aim of obtaining approximate analytic expressions mainly for the energies of the excited states with l≠0. Use is made of the Hypervirial Theorems (HVT) in conjunction with the Hellmann-Feynman Theorem (HFT) which provide a very powerful scheme especially for the treatment of 'Oscillator-like' potentials,as previous studies have shown. The energy eigenvalues are calculated in the form of an expansion, the first terms of which, in many cases, yield very satisfactory results.

scholarly journals Application of the quantum mechanical hypervirial theorems to even-power series potentials

2020 ◽  
Vol 5 ◽  
pp. 104
Author(s):  
T. E. Liolios ◽  
M. E. Grypeos
Keyword(s):  
Power Series ◽  
Excited States ◽  
Energy Operator ◽  
Quantum Mechanical ◽  
Expectation Values ◽  
Gaussian Potential ◽  
Energy Eigenvalues ◽  
The Mean ◽  
Potential Parameters ◽  
Feynman Theorem

The class of the even-power series potentials:V(r)=-D+ Σ_k^{\infty} V_kλ^kr^{2k+2}, Vo=ω^2>0, is studied with the aim of obtaining approximate analytic ex­pressions for the energy eigenvalues, the expectation values for the potential and the kinetic energy operator, and the mean square radii of the orbits of a particle in its ground and excited states. We use the Hypervirial Theorems (HVT) in conjunction with the Hellmann-Feynman Theorem (HFT) which provide a very powerful scheme especially for the treatment of that type of potentials, as previous studies have shown. The formalism is reviewed and the expressions of the above mentioned quantities are subsequently given in a convenient way in terms of the potential parameters and the mass of the particle, and are then applied to the case of the Gaussian potential and to the potential V(r)=-D/cosh^2(r/R). These expressions are given in the form of series expansions, the first terms of which yield in quite a number of cases values of very satisfactory accuracy.

ENTANGLEMENT IN THE XY SPIN CHAIN WITH NONUNIFORM EXTERNAL MAGNETIC FIELDS

2005 ◽  
Vol 03 (03) ◽  
pp. 569-577 ◽  
Author(s):  
JUNPENG CAO ◽  
Z. Z. SUN ◽  
YIN SUN ◽  
YUPENG WANG ◽  
X. R. WANG
Keyword(s):  
Magnetic Fields ◽  
Excited States ◽  
Ground State ◽  
Boundary Effects ◽  
Open Boundary ◽  
Xy Model ◽  
Open Boundary Conditions ◽  
Thermal Entanglement ◽  
Analytic Expressions ◽  
Xy Spin Chain

We study the entanglement in the three-site Heisenberg XY model with nonuniform external magnetic fields and obtain analytic expressions for the measures of entanglement in the system with both the periodic and the open boundary conditions. We show that both the ground state and the excited states of the system possess remarkable entanglement properties and the entanglement clearly depends on the magnitude of external fields. We obtain the pairwise thermal entanglement of the system. We also discuss the boundary effects on the entanglement.

Vibration of Diatomic System in One-Dimensional Nanomaterials

2011 ◽  
Vol 55-57 ◽  
pp. 545-549
Author(s):  
Jun Lu
Keyword(s):  
Bound States ◽  
Hypergeometric Series ◽  
Basis Set ◽  
Eigenvalues And Eigenfunctions ◽  
One Dimensional ◽  
Energy Eigenvalues ◽  
Diatomic System ◽  
Analytic Expressions ◽  
Hyperbolic Potential ◽  
The One

By means of the hypergeometric series method, the explicit expressions of energy eigenvalues and eigenfunctions of bound states for a diatomic system with a hyperbolic potential function are obtained in the one-dimensional nanomaterials. The eigenfunctions of a one-dimensional diatomic system, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.

scholarly journals Analysis of the binding energies of the Λ- particle in hypernuclei with the RHVT approach and the Gauss potential

2019 ◽  
Vol 18 ◽  
pp. 19
Author(s):  
C. A. Efthimiou ◽  
M. E. Grypeos ◽  
C. G. Koutroulos ◽  
Th. Petridou
Keyword(s):  
Relativistic Quantum ◽  
Binding Energies ◽  
Core Mass ◽  
Least Squares Fit ◽  
Power Series Expansions ◽  
Analytic Expressions ◽  
Particle Potential ◽  
Hypervirial Theorem ◽  
Single Particle Potential

An analysis is carried out mainly of the ground state binding energies of the Λ-particle in hypernuclei with values of the core mass number AC between 15 and 207 (included) using, as far as possible, recent experimental data.Τhe renormalized (non- relativistic) quantum mechanical hypervirial theorem (RHVT) technique is employed in the form of s- power series expansions and a Gauss single particle potential for the motion of a Λ- particle in hypernuclei is used. Not exact analytic solution is known for the Schrödinger eigenvalue problem in this case. Thus, the approximate analytic expressions (AAE) for the energy eigenvalues which are obtained with the RHVT approach and are quite useful as long as the involved dimensionless parameter s is sufficiently small, are compared only with the numerical solution. The potential parameters are determined by a least-squares fit in the framework of the rigid core model for the hypernuclei. A discussion is also made regarding the determination of the renormalization parameter χ.

Excited states of even-A and odd-A nuclei with deformation-dependent mass parameters for the Kratzer potential

2021 ◽  
Author(s):  
M. Chabab ◽  
I. El-ilali ◽  
A. Lahbas ◽  
M. Oulne
Keyword(s):  
Experimental Data ◽  
Excited States ◽  
Transition Probabilities ◽  
Energy Spectra ◽  
Asymptotic Iteration Method ◽  
Axially Symmetric ◽  
Electromagnetic Transition ◽  
Energy Eigenvalues ◽  
Dependent Mass ◽  
Davidson Potential

The low-lying collective spectra for axially symmetric nuclei are described within the Bohr–Hamiltonian by considering deformation-dependent mass coefficients and Kratzer potential in [Formula: see text] part. The energy eigenvalues and the total wave function of the problem are obtained in compact forms by means of the asymptotic iteration method. The numerical calculations are carried out for energy spectra as well as electromagnetic transition probabilities, and compared with experimental data in both cases: within and without the deformation-dependent mass (DDM) formalism. We investigate the nuclear observables of four even-A nuclei [Formula: see text]Sm, [Formula: see text]Gd, [Formula: see text]Yb, [Formula: see text]W and two odd-A nuclei [Formula: see text]Yb, [Formula: see text]Dy. Moreover, we will show that the choice of the Kratzer potential minimizes the level spacings within the [Formula: see text] band, which are usually overestimated by Bohr–Hamiltonian with Davidson potential.

scholarly journals On a single particle potential for atomic clusters

2020 ◽  
Vol 9 ◽  
pp. 307
Author(s):  
B. A. Kotsos ◽  
Th. E. Liolios ◽  
M. E. Grypeos ◽  
C. G. Koutroulos ◽  
S. E. Massen
Keyword(s):  
Single Particle ◽  
Metal Clusters ◽  
Atomic Clusters ◽  
Energy Eigenvalues ◽  
Valence Electrons ◽  
Analytic Expressions ◽  
Particle Potential ◽  
Single Particle Potential

The single-particle potential V(r) = -Vo[1+(r/K)^β)^-1, which has been proposed in the recent years for atomic (metal) clusters, is studied analytically in the case β = 2. By using perturbation-type techniques, approximate analytic expressions are obtained for the energy eigenvalues and other physically interesting quantities showing the variation of these quantities with the number of valence electrons. The accuracy is tested for Al clusters and is usually very good.

Large-N Expansion for a Nucleon-Nucleon Potential

1989 ◽  
Vol 44 (11) ◽  
pp. 1137-1138 ◽  
Author(s):  
Fevzi Büyükkilic ◽  
Dogan Demirhan
Keyword(s):  
Schrödinger Equation ◽  
Excited States ◽  
Schrodinger Equation ◽  
Yukawa Potential ◽  
Nucleon Nucleon ◽  
Nucleon System ◽  
Nucleon Potential ◽  
Energy Eigenvalues ◽  
Large N ◽  
Large N Expansion

Abstract The Schrödinger equation has been solved by \/N expan­ sion for a two nucleon system which interacts by an attrac­ tive Yukawa potential. For the ground and first excited states, energy eigenvalues have been obtained.

scholarly journals Symmetry resolved relative entropies and distances in conformal field theory

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Luca Capizzi ◽  
Pasquale Calabrese
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Excited States ◽  
Total System ◽  
Conformal Field ◽  
Analytic Expressions ◽  
Remarkable Result ◽  
Single Interval ◽  
Reduced Density ◽  
Twist Fields

Abstract We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory having an internal U(1) symmetry. We provide analytic expressions for the charged moments corresponding to the resolution of both relative entropies and distances for general integer n. For the relative entropies, these formulas are manageable and the analytic continuation to n = 1 can be worked out in most of the cases. Conversely, for the distances the corresponding charged moments become soon untreatable as n increases. A remarkable result is that relative entropies and distances are the same for all symmetry sectors, i.e. they satisfy entanglement equipartition, like the entropies. Moreover, we exploit the OPE expansion of composite twist fields, to provide very general results when the subsystem is a single interval much smaller than the total system. We focus on the massless compact boson and our results are tested against exact numerical calculations in the XX spin chain.

PHENOMENOLOGICAL RELATIVISTIC STUDY OF THE ENERGY OF A Λ IN ITS GROUND AND EXCITED STATES IN HYPERNUCLEI

1994 ◽  
Vol 03 (03) ◽  
pp. 939-951
Author(s):  
G.J. PAPADOPOULOS ◽  
C.G. KOUTROULOS ◽  
M.E. GRYPEOS
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Dirac Equation ◽  
Least Squares ◽  
Excited States ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Small Component ◽  
Repulsive Potentials ◽  
Analytic Expressions

The binding energy BΛ of a Λ-particle in hypernuclei is studied by means of the Dirac equation with attractive and repulsive potentials of rectangular shapes and of the same radius. The energy eigenvalue equation in this case is obtained analytically for every bound state, as well as the large and small component of the wave function (for given BΛ). A first attempt is also made to investigate the possibility of deriving in particular cases approximate analytic expressions of BΛ for the excited states. Using various least squares fittings, numerical results for the binding energy of the Λ are given and comparisons and comments are also made.

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