scholarly journals Bound State of Heavy Quarks Using a General Polynomial Potential

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Hesham Mansour ◽  
Ahmed Gamal
Keyword(s):  
Bound States ◽  
Bound State ◽  
Heavy Quarks ◽  
Polynomial Potential ◽  
Schrödinger’S Equation ◽  
General Polynomial ◽  
L Value ◽  
Schrödinger's Equation ◽  
Better Than ◽  
Good Agreement

In the present work, the mass spectra of the bound states of heavy quarks cc-,bb-, and Bc meson are studied within the framework of the nonrelativistic Schrödinger’s equation. First, we solve Schrödinger’s equation with a general polynomial potential by Nikiforov-Uvarov (NU) method. The energy eigenvalues for any L- value is presented for a special case of the potential. The results obtained are in good agreement with the experimental data and are better than previous theoretical studies.

scholarly journals Spin Splitting Spectroscopy of Heavy Quark and Antiquarks Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hesham Mansour ◽  
Ahmed Gamal ◽  
M. Abolmahassen
Keyword(s):  
Mass Spectra ◽  
Bound States ◽  
Good Accuracy ◽  
Theoretical Calculations ◽  
Spin Splitting ◽  
Energy Eigenvalues ◽  
Central Case ◽  
Nu Method ◽  
Better Than ◽  
Good Agreement

Phenomenological potentials describe the quarkonium systems like c c ¯ , b b , ¯   and   b ¯ c where they give a good accuracy for the mass spectra. In the present work, we extend one of our previous works in the central case by adding spin-dependent terms to allow for relativistic corrections. By using such terms, we get better accuracy than previous theoretical calculations. In the present work, the mass spectra of the bound states of heavy quarks   c c ¯ , b b ¯ , and 𝐵𝑐 mesons are studied within the framework of the nonrelativistic Schrödinger equation. First, we solve Schrödinger’s equation by Nikiforov-Uvarov (NU) method. The energy eigenvalues are presented using our new potential. The results obtained are in good agreement with the experimental data and are better than the previous theoretical estimates.

scholarly journals Exact and approximate solutions to Schrödinger’s equation with decatic potentials

Open Physics ◽  
2013 ◽  
Vol 11 (3) ◽  
Author(s):  
David Brandon ◽  
Nasser Saad
Keyword(s):  
Sufficient Conditions ◽  
Approximate Solutions ◽  
Asymptotic Iteration Method ◽  
Polynomial Potential ◽  
Schrödinger’S Equation ◽  
Polynomial Solutions ◽  
Polynomial Coefficients ◽  
Linear Differential ◽  
Polynomial Potentials ◽  
Schrödinger's Equation

AbstractThe one-dimensional Schrödinger’s equation is analysed with regard to the existence of exact solutions for decatic polynomial potentials. Under certain conditions on the potential’s parameters, we show that the decatic polynomial potential V (x) = ax 10 + bx 8 + cx 6 + dx 4 + ex 2, a > 0 is exactly solvable. By examining the polynomial solutions of certain linear differential equations with polynomial coefficients, the necessary and sufficient conditions for corresponding energy-dependent polynomial solutions are given in detail. It is also shown that these polynomials satisfy a four-term recurrence relation, whose real roots are the exact energy eigenvalues. Further, it is shown that these polynomials generate the eigenfunction solutions of the corresponding Schrödinger equation. Further analysis for arbitrary values of the potential parameters using the asymptotic iteration method is also presented.

scholarly journals A new implicit symmetric method of sixth algebraic order with vanished phase-lag and its first derivative for solving Schrödinger's equation

2021 ◽  
Vol 19 (1) ◽  
pp. 225-237
Author(s):  
Saleem Obaidat ◽  
Rizwan Butt
Keyword(s):  
Phase Lag ◽  
Step Method ◽  
Method Performance ◽  
Schrödinger’S Equation ◽  
First Derivative ◽  
Algebraic Order ◽  
The One ◽  
Schrödinger's Equation ◽  
Better Than ◽  
Symmetric Method

Abstract In this article, we have developed an implicit symmetric four-step method of sixth algebraic order with vanished phase-lag and its first derivative. The error and stability analysis of this method are investigated, and its efficiency is tested by solving efficiently the one-dimensional time-independent Schrödinger’s equation. The method performance is compared with other methods in the literature. It is found that for this problem the new method performs better than the compared methods.

BEHAVIOR OF SOUND WAVES IN SHEPHERD FLUTE ON THE BASIS OF QUANTUM THEORY OF INDIVIDUAL PHONONS

2010 ◽  
Vol 24 (17) ◽  
pp. 3439-3452
Author(s):  
SONJA KRSTIĆ ◽  
VJEKOSLAV SAJFERT ◽  
BRATISLAV TOŠIĆ
Keyword(s):  
Quantum Theory ◽  
Hyperbolic Equation ◽  
Plane Waves ◽  
Sound Waves ◽  
High Frequencies ◽  
Schrödinger’S Equation ◽  
Schrödinger's Equation ◽  
Theory And Experiment ◽  
Good Agreement

Using the linearized Hamiltonian of individual phonon, it was shown that Schrödinger's equation of individual phonon is by form identical with classical hyperbolic equation. It was also shown that damper in shepherd's flute is reflexive for high frequencies and transparent for low ones. This result was experimentally tested by authors and good agreement of theory and experiment was found. The propagation of sound in parallelopipedal and cylindrical shepherd's flute was investigated. It turned out that parallelopipedal sound propagates in z-direction, only, while in cylindrical one besides plane waves in z-direction the damped waves in x, y plane appear.

scholarly journals NEW BOUND STATES OF HEAVY QUARKS AT LHC AND TEVATRON

2011 ◽  
Vol 26 (15) ◽  
pp. 2503-2521 ◽  
Author(s):  
C. R. DAS ◽  
C. D. FROGGATT ◽  
L. V. LAPERASHVILI ◽  
H. B. NIELSEN
Keyword(s):  
Top Quark ◽  
Bound States ◽  
Form Factors ◽  
Top Quarks ◽  
Bound State ◽  
Heavy Quarks ◽  
Fourth Generation ◽  
Charge Multiplicity ◽  
The Masses ◽  
B Quark

The present paper is based on the assumption that heavy quarks bound states exist in the Standard Model (SM). Considering New Bound States (NBS) of top–antitop quarks (named T-balls) we have shown that: (1) there exists the scalar 1S-bound state of [Formula: see text]; (2) the forces which bind the top-quarks are very strong and almost completely compensate the mass of the twelve top–antitop-quarks in the scalar NBS; (3) such strong forces are produced by the Higgs–top-quarks interaction with a large value of the top-quark Yukawa coupling constant gt≃1. Theory also predicts the existence of the NBS [Formula: see text], which is a color triplet and a fermion similar to the t'-quark of the fourth generation. We have also considered the "b-quark-replaced" NBS, estimated the masses of the lightest fermionic NBS: M NBS ≳300 GeV , and discussed the larger masses of T-balls. We have developed a theory of the scalar T-ball's condensate and predicted the existence of three SM phases. Searching for heavy quark bound states at the Tevatron and LHC is discussed. We have constructed the possible form-factors of T-balls, and estimated the charge multiplicity coming from the T-ball's decays.

scholarly journals A balanced-to-balanced directional coupler based on branch-slotline coupled structure

Frequenz ◽  
2020 ◽  
Vol 74 (11-12) ◽  
pp. 427-433
Author(s):  
Yaxin Liu ◽  
Feng Wei ◽  
Xiaowei Shi ◽  
Cao Zeng
Keyword(s):  
Directional Coupler ◽  
Return Loss ◽  
Design Method ◽  
Differential Mode ◽  
Arbitrary Power ◽  
Measurement Results ◽  
Transition Structures ◽  
Coupled Structures ◽  
Better Than ◽  
Good Agreement

AbstractIn this paper, a balanced-to-balanced (BTB) branch-slotline directional coupler (DC) is firstly presented, which can realize an arbitrary power division ratios (PDRs). The coupler is composed by microstrip-to-slotline (MS) transition structures and branch-slotline coupled structures. The single-ended to balanced-ended conversion is simplified and easy to implemented by the MS transition structures, which intrinsically leads to the differential-mode (DM) transmission and common-mode (CM) suppression. Moreover, the different PDRs which are controlled by the widths of branch-slotlines can be achieved. In order to verify the feasibility of the proposed design method, two prototype circuits of the proposed coupler with different PDRs are fabricated and measured. The return loss and the isolation of two designs are all better than 10 dB. Moreover, the CM suppressions are greater than 35 dB. A good agreement between the simulation and measurement results is observed.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

scholarly journals A high-fidelity realization of the Euclid code comparison N-body simulation with Abacus

2019 ◽  
Vol 485 (3) ◽  
pp. 3370-3377 ◽  
Author(s):  
Lehman H Garrison ◽  
Daniel J Eisenstein ◽  
Philip A Pinto
Keyword(s):  
Power Spectrum ◽  
High Performance ◽  
High Fidelity ◽  
Step Size ◽  
Time Step ◽  
Code Comparison ◽  
Force Accuracy ◽  
Integration Errors ◽  
Better Than ◽  
Good Agreement

Abstract We present a high-fidelity realization of the cosmological N-body simulation from the Schneider et al. code comparison project. The simulation was performed with our AbacusN-body code, which offers high-force accuracy, high performance, and minimal particle integration errors. The simulation consists of 20483 particles in a $500\ h^{-1}\, \mathrm{Mpc}$ box for a particle mass of $1.2\times 10^9\ h^{-1}\, \mathrm{M}_\odot$ with $10\ h^{-1}\, \mathrm{kpc}$ spline softening. Abacus executed 1052 global time-steps to z = 0 in 107 h on one dual-Xeon, dual-GPU node, for a mean rate of 23 million particles per second per step. We find Abacus is in good agreement with Ramses and Pkdgrav3 and less so with Gadget3. We validate our choice of time-step by halving the step size and find sub-percent differences in the power spectrum and 2PCF at nearly all measured scales, with ${\lt }0.3{{\ \rm per\ cent}}$ errors at $k\lt 10\ \mathrm{Mpc}^{-1}\, h$. On large scales, Abacus reproduces linear theory better than 0.01 per cent. Simulation snapshots are available at http://nbody.rc.fas.harvard.edu/public/S2016.

THEORETICAL CALCULATION OF pKb VALUES FOR ANILINES AND SULFONAMIDE DRUGS IN AQUEOUS SOLUTION

2012 ◽  
Vol 11 (02) ◽  
pp. 283-295 ◽  
Author(s):  
BAHRAM GHALAMI-CHOOBAR ◽  
ALI GHIAMI-SHOMAMI ◽  
PARIA NIKPARSA
Keyword(s):  
Gas Phase ◽  
Continuum Model ◽  
Correlation Equation ◽  
Polarizable Continuum Model ◽  
Free Energies ◽  
Pcm Model ◽  
Solvation Models ◽  
Polarizable Continuum ◽  
Better Than ◽  
Good Agreement

In this work, calculations of p K b values have been performed for aniline and its substituted derivatives and sulfonamide drugs by using Gaussian 98 software package. Gas-phase energies were calculated with HF /6-31 G ** and B3LYP /6-31 G ** levels of theory. Free energies of solvation have been computed using the polarizable continuum model (PCM), conductor-like polarizable continuum model (CPCM) and the integral equation formalism-polarizable continuum model (IEFPCM) at the same levels which have been used for geometry determination in the gas-phase. The results show that the calculated p K b values using the B3LYP /6-31 G ** are better than those using the corresponding HF /6-31 G **. At first, the correlation equation was found to determine the p K b values of the investigated anilines. Then, this correlation equation was used to calculate the p K b values of the sulfonamide drugs. The results obtained indicate that the PCM model is a suitable solvation model for calculating p K b values in comparison to the other solvation models. For the investigated compounds a good agreement between the experimental and the calculated p K b values was also observed.

Sign in / Sign up

Export Citation Format

Share Document