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## Bounds for the signless laplacian energy

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

ENG

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55.85%

#Graph spectrum#Laplacian energy#Laplacian graph spectrum#Signless Laplacian energy#Signless Laplacian spectrum#Absolute values#Adjacency matrices#Arithmetic mean#Eigenvalues#Energy of a graph#Graph spectra

The energy of a graph G is the sum of the absolute values of the eigenvalues of the adjacency matrix of G. The Laplacian (respectively, the signless Laplacian) energy of G is the sum of the absolute values of the differences between the eigenvalues of the Laplacian (respectively, signless Laplacian) matrix and the arithmetic mean of the vertex degrees of the graph. In this paper, among some results which relate these energies, we point out some bounds to them using the energy of the line graph of G. Most of these bounds are valid for both energies, Laplacian and signless Laplacian. However, we present two new upper bounds on the signless Laplacian which are not upper bounds for the Laplacian energy. © 2010 Elsevier Inc. All rights reserved.; FCT; FEDER/POCI 2010; CNPq; PQ-305016/2006–2007; Serbian Ministry of Science; No. 144015G; Mecesup 2 UCN 0605; Fondecyt-IC Project 11090211

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## First Principles Semiclassical Calculations of Vibrational Eigenfunctions

Fonte: American Institute of Physics
Publicador: American Institute of Physics

Tipo: Artigo de Revista Científica

EN_US

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75.91%

#carbon compounds#chemisorption#copper#density functional theory#eigenvalues and eigenfunctions#initial value problems#potential energy surfaces#vibrational states#ab initio calculations

Vibrational eigenfunctions are calculated on-the-fly using semiclassical methods in conjunction with ab initio density functional theory classical trajectories. Various semiclassical approximations based on the time-dependent representation of the eigenfunctions are tested on an analytical potential describing the chemisorption of CO on Cu(100). Then, first principles semiclassical vibrational eigenfunctions are calculated for the (CO_2) molecule and its accuracy evaluated. The multiple coherent states initial value representations semiclassical method recently developed by us has shown with only six ab initio trajectories to evaluate eigenvalues and eigenfunctions at the accuracy level of thousands trajectory semiclassical initial value representation simulations.; Chemistry and Chemical Biology

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## Energy spectrum and eigenfunctions through the Quantum Section Method

Fonte: Sociedade Brasileira de Física
Publicador: Sociedade Brasileira de Física

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/12/2001
EN

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We present the Quantum Section Method as a quantization technique to compute the eigenvalues and the eigenfunctions of quantum systems. As an instructive example we apply this procedure to quantize the annular billiard. The method uses the symmetry of the system to determine an auxiliary section separating the system into partial regions and computes the Green's functions for Schroedinger's equation, obeying the same boundary conditions imposed on the eigenfunctions of the system. The eigenvalues are obtained as zeroes of a finite real determinant and the eigenfunctions are also determined. The present analytical and numerical results are in total agreement with those obtained by other procedures, which shows the efficiency of the method.

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## On the $\kappa$-Dirac Oscillator revisited

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

55.84%

This Letter is based on the $\kappa$-Dirac equation, derived from the
$\kappa$-Poincar\'{e}-Hopf algebra. It is shown that the $\kappa$-Dirac
equation preserves parity while breaks charge conjugation and time reversal
symmetries. Introducing the Dirac oscillator prescription,
$\mathbf{p}\to\mathbf{p}-im\omega\beta\mathbf{r}$, in the $\kappa$-Dirac
equation, one obtains the $\kappa$-Dirac oscillator. Using a decomposition in
terms of spin angular functions, one achieves the deformed radial equations,
with the associated deformed energy eigenvalues and eigenfunctions. The
deformation parameter breaks the infinite degeneracy of the Dirac oscillator.
In the case where $\varepsilon=0$, one recovers the energy eigenvalues and
eigenfunctions of the Dirac oscillator.; Comment: 5 pages, no figures, accepted for publication in Physics Letters B

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## Eigenvalues and Eigenfunctions of the Scalar Laplace Operator on Calabi-Yau Manifolds

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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75.83%

A numerical algorithm for explicitly computing the spectrum of the
Laplace-Beltrami operator on Calabi-Yau threefolds is presented. The requisite
Ricci-flat metrics are calculated using a method introduced in previous papers.
To illustrate our algorithm, the eigenvalues and eigenfunctions of the
Laplacian are computed numerically on two different quintic hypersurfaces, some
Z_5 x Z_5 quotients of quintics, and the Calabi-Yau threefold with Z_3 x Z_3
fundamental group of the heterotic standard model. The multiplicities of the
eigenvalues are explained in detail in terms of the irreducible representations
of the finite isometry groups of the threefolds.; Comment: 67 pages, 16 figures, 9 tables. v2: References added

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## Exact Ultra Cold Neutrons' Energy Spectrum in Gravitational Quantum Mechanics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/09/2013

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65.66%

We find exact energy eigenvalues and eigenfunctions of the quantum bouncer in
the presence of the minimal length uncertainty and the maximal momentum. This
form of Generalized (Gravitational) Uncertainty Principle (GUP) agrees with
various theories of quantum gravity and predicts a minimal length uncertainty
proportional to $\hbar\sqrt{\beta}$ and a maximal momentum proportional to
$1/\sqrt{\beta}$, where $\beta$ is the deformation parameter. We also find the
semiclassical energy spectrum and discuss the effects of this GUP on the
transition rate of the ultra cold neutrons in gravitational spectrometers.
Then, based on the Nesvizhevsky's famous experiment, we obtain an upper bound
on the dimensionless GUP parameter.; Comment: 11 pages, 1 figure, to appear in European Physical Journal C

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## On Eigenvalues and Eigenfunctions Absent in the Actual Solid State Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/09/2000

Relevância na Pesquisa

65.92%

In this letter new, closed and compact analytic expressions for the
evaluation of resonant energies, resonant bound-states, eigenvalues and
eigenfunctions for both scattering and bounded $n$-cell systems are reported.
It is shown that for (scattering and bounded) 1-D systems the eigenfunctions
$\Psi_{\mu ,\nu}(z)$ are simple and well defined functions of the Chebyshev
polynomials of the second kind $U_{n}$, and the energy eigenvalues $E_{\mu ,\nu
}$ (in the $\mu $-th band) are determined by the zeros of these polynomials.
New insights on the energy gap and the localization effect induced by phase
coherence are shown.; Comment: 10 pages, 5 figures

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## Accurate energy spectrum for the quantum Yang-Mills mechanics with nonlinear color oscillations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/05/2014

Relevância na Pesquisa

65.65%

Yang-Mills theory as the foundation for quantum chromodynamics is a
non-Abelian gauge theory with self-interactions between vector particles. Here,
we study the Yang-Mills Hamiltonian with nonlinear color oscillations in the
absence of external sources corresponding to the group $SU(2)$. In the quantum
domain, we diagonalize the Hamiltonian using the optimized trigonometric basis
expansion method and find accurate energy eigenvalues and eigenfunctions for
one and two degrees of freedom. We also compare our results with the
semiclassical solutions.; Comment: 12 pages, 2 figures, to appear in International Journal of
Theoretical Physics

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## The effects of minimal length and maximal momentum on the transition rate of ultra cold neutrons in gravitational field

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/03/2011

Relevância na Pesquisa

65.62%

The existence of a minimum observable length and/or a maximum observable
momentum is in agreement with various candidates of quantum gravity such as
string theory, loop quantum gravity, doubly special relativity and black hole
physics. In this scenario, the Heisenberg uncertainty principle is changed to
the so-called Generalized (Gravitational) Uncertainty Principle (GUP) which
results in modification of all Hamiltonians in quantum mechanics. In this
paper, following a recently proposed GUP which is consistent with quantum
gravity theories, we study the quantum mechanical systems in the presence of
both a minimum length and a maximum momentum. The generalized Hamiltonian
contains two additional terms which are proportional to $\alpha p^3$ and
$\alpha^2 p^4$ where $\alpha \sim 1/M_{Pl}c$ is the GUP parameter. For the case
of a quantum bouncer, we solve the generalized Schrodinger equation in the
momentum space and find the modified energy eigenvalues and eigenfunctions up
to the second-order in GUP parameter. The effects of the GUP on the transition
rate of ultra cold neutrons in gravitational spectrometers are discussed
finally.; Comment: 13 pages, 1 figure, to appear in JHEP

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## High-Precision Numerical Determination of Eigenvalues for a Double-Well Potential Related to the Zinn-Justin Conjecture

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

65.71%

A numerical method of high precision is used to calculate the energy
eigenvalues and eigenfunctions for a symmetric double-well potential. The
method is based on enclosing the system within two infinite walls with a large
but finite separation and developing a power series solution for the
Schr$\ddot{o}$dinger equation. The obtained numerical results are compared with
those obtained on the basis of the Zinn-Justin conjecture and found to be in an
excellent agreement.; Comment: Substantial changes including the title and the content of the paper
8 pages, 2 figures, 3 tables

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## Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

75.78%

Spin-weighted spheroidal harmonics are useful in a variety of physical
situations, including light scattering, nuclear modeling, signal processing,
electromagnetic wave propagation, black hole perturbation theory in four and
higher dimensions, quantum field theory in curved space-time and studies of
D-branes. We first review analytic and numerical calculations of their
eigenvalues and eigenfunctions in four dimensions, filling gaps in the existing
literature when necessary. Then we compute the angular dependence of the
spin-weighted spheroidal harmonics corresponding to slowly-damped quasinormal
mode frequencies of the Kerr black hole, providing numerical tables and
approximate formulas for their scalar products. Finally we present an
exhaustive analytic and numerical study of scalar spheroidal harmonics in (n+4)
dimensions.; Comment: 26 pages, 10 figures. Corrected typos in Eqs. (2.16f) and (2.16g)

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## Eigenvalues and Eigenfunctions of Woods Saxon Potential in PT Symmetric Quantum Mechanics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

65.78%

Using the Nikiforov Uvarov method, we obtained the eigenvalues and
eigenfunctions of the Woods Saxon potential with the negative energy levels
based on the mathematical approach. According to the PT Symmetric quantum
mechanics, we exactly solved the time independent Shcrodinger equation for the
same potential. Results are obtained for the s states.; Comment: 12 pages. submitted to Physics Letters A

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## One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

65.64%

We present exact energy eigenvalues and eigenfunctions of the one-dimensional
hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty
Principle (GUP). This form of GUP is consistent with various theories of
quantum gravity such as string theory, loop quantum gravity, black-hole
physics, and doubly special relativity and implies a minimal length uncertainty
and a maximal momentum. We show that the quantized energy spectrum exactly
agrees with the semiclassical results.; Comment: 10 pages, 1 figure

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## Cosmic censorship and stationary states of half-spin particles in the field of Reissner-Nordstroem naked singularity

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/11/2015

Relevância na Pesquisa

65.59%

The paper explores quantum mechanics of half-spin particle motion in the
field of Reissner-Nordstroem (RN) naked singularity. It is shown that for any
quantum mechanical Dirac particle, irrespective of availability and sign of its
electrical charge, the RN naked singularity is separated by an infinitely high
positive potential barrier. With like charges of a particle and the source of
the RN naked singularity, near the origin there exists the second completely
impenetrable potential barrier. It has been proved that in the field of the RN
naked singularity, bound states of half-spin particles can exist. The
conditions for appearance of such states were revealed and computations were
performed to find energy eigenvalues and eigenfunctions.; Comment: 20 pages, 3 figures

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## Property of Zero-Energy Flows and Creations and Annihilations of Vortices in Quantum Mechanics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

55.92%

Time-dependent processes accompanied by vortex creations and annihilations
are investigated in terms of the eigenstates in conjugate spaces of Gel'fand
triplets in 2-dimensions. Creations and annihilations of vortices are described
by the insertions of unstable eigenstates with complex-energy eigenvalues into
stable states written by the superposition of eigenstates with zero-energy
eigenvalues. Some concrete examples are presented in terms of the
eigenfunctions of the 2-dimensional parabolic potential barrier, i.e., $-m
\gamma^2 (x^2+y^2)/2$. We show that the processes accompanied by vortex
creations and annihilations can be analyzed in terms of the eigenfunctions in
the conjugate spaces of Gel'fand triplets. Throughout these examinations we
point out three interesting properties of the zero-energy flows. (i) Mechanisms
using the zero-energy flows are absolutely economical from the viewpoint of
energy consumption. (ii) An enormous amount of informations can be
discriminated in terms of the infinite variety of the zero-energy flows. (iii)
The zero-energy flow patterns are absolutely stable in any disturbance by
inserting arbitrary decaying flows with complex-energy eigenvalues.; Comment: 13 pages and 13 figures

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## Accurate calculation of eigenvalues and eigenfunctions. I: Symmetric potentials

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

65.72%

We describe a method for the calculation of accurate energy eigenvalues and
expectation values of observables of separable quantum-mechanical models. We
discuss the application of the approach to one-dimensional anharmonic
oscillators with symmetric potential-energy functions.

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## Exact Eigenvalues and Eigenfunctions of the Hulthen Potential in the PT-Symmetry for Any Angular Momentum

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/08/2005

Relevância na Pesquisa

75.84%

The Schrodinger equation with the PT-symmetric Hulthen potential is solved
exactly by taking into account effect of the centrifugal barrier for any
l-state. Eigenfunctions are obtained in terms of the Jacobi polynomials. The
Nikiforov-Uvarov method is used in the computations. Our numerical results are
in good agreement with the ones obtained before.
Keywords: Energy Eigenvalues and Eigenfunctions; Hulthen potential;
PT-symmetry; Nikiforov-Uvarov Method.; Comment: 24 pages

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## Thouless Energy and Correlations of QCD Dirac Eigenvalues

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

55.81%

Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for
gauge field configurations given by a liquid of instantons. We find that for
energy differences $\delta E$ below an energy scale $E_c$ the eigenvalue
correlations are given by Random Matrix Theories with the chiral symmetries of
the QCD partition function. For eigenvalues near zero this energy scale shows a
weak volume dependence that is not consistent with $E_c \sim 1/L^2$ which might
be expected from the pion Compton wavelength and from the behavior of the
Thouless energy in mesoscopic systems. However, the numerical value of $E_c$
for our largest volumes is in rough agreement with estimates from the pion
Compton wavelength. A scaling behaviour consistent with $E_c\sim 1/L^2$ is
found in the bulk of the spectrum. For $\delta E> E_c$ the number variance
shows a linear dependence with a slope which is larger than the nonzero
multifractality index of the wave functions. Finally, the average spectral
density and the scalar susceptibilities are discussed in the context of
quenched chiral perturbation theory. We argue that a nonzero value of the
disconnected scalar susceptibility requires a linear dependence of the number
variance on $\delta E$.; Comment: 19 pages...

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## Coupled diabatic potential energy surfaces for studying the nonadiabatic dynamics at conical intersections in angular resolved photodetachment simulations of OHF- --> OHF+e-

Fonte: American Institute of Physics
Publicador: American Institute of Physics

Tipo: Artículo
Formato: 1553773 bytes; application/pdf

ENG

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#Oxygen compounds#Fluorine#Electron detachment#Potential energy surfaces#Atom-molecule reactions#Reaction kinetics#Ab initio calculations#Eigenvalues and eigenfunctions#Triplet state#Molecule-photon collisions#[PACS] Potential energy surfaces for chemical reactions

16 pages, 14 figures, 1 table.-- PACS nrs.: 82.20.Kh; 82.30.Cf; 33.80.Eh; 82.20.Db; 82.20.Hf.; An energy-based method is proposed for the diabatization of the OH(2Π)+F(2P) --> O(3P)+HF(1Σ+) reaction. It is demonstrated that the diabatic representation obtained is regularized, i.e., the residual derivative couplings do not present singularities at the conical intersections appearing along the reaction path. This method only requires the knowledge of the 1,2 3A'' and 1 3A' eigenvalues and does not require any adjustable parameter. Thus, many convergence problems arising in other derivative-based diabatization methods are avoided, and the description of the configuration space along the reaction path is enormously simplified. Three-dimensional coupled diabatic energy surfaces are obtained by an interpolation procedure using ≈ 4000 accurate ab initio points. The angular resolved photodetachment cross sections are obtained in the diabatic and adiabatic representations using a wave packet method. An excellent agreement is obtained with recent experimental data [D. M. Neumark, Phys. Chem. Chem. Phys. 7, 433 (2005)] for high electron kinetic energies where only the triplet electronic states contribute.; This work has been supported by DGICYT (Ministerio de Educación y Ciencia...

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## Energy eigenvalues for free and confined triple-well potentials

Fonte: Sociedad Mexicana de Física
Publicador: Sociedad Mexicana de Física

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/02/2011
EN

Relevância na Pesquisa

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#One-dimensional triple-well potentials#energy eigenvalues and eigenfunctions#confined quantum systems

Some confined and unconfined (free) one-dimensional triple-well potentials are analyzed with two different numerical approaches. Confinement is achieved by enclosing the potential between two impenetrable walls. The unconfined (free) system is recovered as the positions of the walls move to infinity. The numerical solutions of the Schrodinger equation for the symmetric and asymmetric potentials without confinement, are comparable in precision with those obtained anaylitically. For the symmetric triple-well potentials, V (x) = αx2 - βx4 + x6, it is found that there are sets of two or three quasi-degenerate eigenvalues depending on the parameters a and ¡3. A heuristic analysis shows that if the conditions α= (β2 /4) ± 1 (with α > 0 and β > 0) are satisfied, then there are sets of three eigenvalues with similar energy. An interesting behavior is found when one impenetrable wall is fixed and the other is moved to different positions. In summary, the number of local minima that the potential has in the confined region determines a two- or three-fold degeneracy.

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