scholarly journals TOWARDS RELIABLE CALCULATIONS OF THE CORRELATION FUNCTION

2007 ◽  
Vol 16 (10) ◽  
pp. 3244-3261 ◽  
Author(s):  
RADOSŁAW MAJ ◽  
STANISŁAW MRÓWCZYŃSKI
Keyword(s):  
Wave Function ◽  
Correlation Function ◽  
Coulomb Interaction ◽  
Relative Motion ◽  
Coulomb Potential ◽  
Center Of Mass ◽  
Relativistic Effects ◽  
Life Time ◽  
Large Domain ◽  
Mass Frame

The correlation function of two identical pions interacting via Coulomb potential is computed for a general case of anisotropic particle's source of finite life time. The effect of halo is taken into account as an additional particle's source of large spatial extension. Due to the Coulomb interaction, the effect of halo is not limited to very small relative momenta but it influences the correlation function in a relatively large domain. The relativistic effects are discussed in detail and it is argued that the calculations have to be performed in the center-of-mass frame of particle's pair where the (nonrelativistic) wave function of particle's relative motion is meaningful. The Bowler–Sinyukov procedure to remove the Coulomb interaction is tested and it is shown to significantly underestimate the source's life time.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

scholarly journals Direct measurement of Coulomb-laser coupling

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Doron Azoury ◽  
Michael Krüger ◽  
Barry D. Bruner ◽  
Olga Smirnova ◽  
Nirit Dudovich
Keyword(s):  
Coulomb Interaction ◽  
Time Domain ◽  
Coulomb Potential ◽  
Laser Field ◽  
Large Range ◽  
Extreme Ultraviolet ◽  
Strong Field ◽  
The Time Domain ◽  
First Time ◽  
Insight Into

AbstractThe Coulomb interaction between a photoelectron and its parent ion plays an important role in a large range of light-matter interactions. In this paper we obtain a direct insight into the Coulomb interaction and resolve, for the first time, the phase accumulated by the laser-driven electron as it interacts with the Coulomb potential. Applying extreme-ultraviolet interferometry enables us to resolve this phase with attosecond precision over a large energy range. Our findings identify a strong laser-Coulomb coupling, going beyond the standard recollision picture within the strong-field framework. Transformation of the results to the time domain reveals Coulomb-induced delays of the electrons along their trajectories, which vary by tens of attoseconds with the laser field intensity.

THE STEREODYNAMICS STUDY OF THE C(3P) + OH (X2 Π) → CO(X1Σ+) + H(2S) REACTION

2010 ◽  
Vol 09 (05) ◽  
pp. 935-943 ◽  
Author(s):  
PENG SONG ◽  
YONG-HUA ZHU ◽  
JIAN-YONG LIU ◽  
FENG-CAI MA
Keyword(s):  
Angular Momentum ◽  
Cross Sections ◽  
Collision Energy ◽  
Energy Surface ◽  
Center Of Mass ◽  
Title Reaction ◽  
High Collision Energy ◽  
Dependency Relationship ◽  
Energy Dependency ◽  
Mass Frame

The stereodynamics of the title reaction on the ground electronic state X2A' potential energy surface (PES)1 has been studied using the quasiclassical trajectory (QCT) method. The commonly used polarization-dependent differential cross-sections (PDDCSs) of the product and the angular momentum alignment distribution, P(θr) and P(Φr), are generated in the center-of-mass frame using QCT method to gain insight of the alignment and orientation of the product molecules. Influence of collision energy on the stereodynamics is shown and discussed. The results reveal that the distribution of P(θr) and P(Φr) is sensitive to collision energy. The PDDCSs exhibit different collision energy dependency relationship at low and high collision energy ranges.

Measurement of the Cross Section for the Process $${e^{+}e^{-}}{\to}{K}^{{+}}{K}^{{-}}{\pi}^{{0}}$$ with the SND Detector at Collision Energies of $$\sqrt{{s}}{=}{1.3{-}2.0}$$ GeV in the Center-of-Mass Frame

2021 ◽  
Vol 84 (1) ◽  
pp. 59-62
Author(s):  
M. N. Achasov ◽  
A. Yu. Barnyakov ◽  
M. Yu. Barnyakov ◽  
K. I. Beloborodov ◽  
A. V. Berdyugin ◽  
...  
Keyword(s):  
Cross Section ◽  
Center Of Mass ◽  
Mass Frame ◽  
The Cross

The Hidden Variables Theory

2021 ◽  
Author(s):  
Israel Fried
Keyword(s):  
Wave Function ◽  
Magnetic Flux ◽  
W Boson ◽  
Energy Levels ◽  
Center Of Mass ◽  
Hidden Variables ◽  
Bound State ◽  
Electron Mass ◽  
Charged Mesons ◽  
New Variables

The book presents a new concept on several physics topics. The initial values are non-relativistic quantities of subatomic particles which the values obtained in experiments are actually their relativistic reflection. The subjects in the book are presented in such order that each new topic is based on the development of its predecessor that explains where it stems from. The book presents methods of analyzing traditional physics concepts to extract hidden embedded information that reveals new variables which are combined with those known. The new formulas yield results that match experiments accurately. It presents discoveries as: The electric charge of subatomic particle results directly from its OAM (Orbital Angular Momentum). OAM Offset exhibits neutral state. The electron mass is a magnitude that expresses quantitatively the square of its magnetic flux quantum, hence this mass in the Wave Function yields solutions that their squared values represent the flow pattern of magnetic flux surrounding electrons at energy levels, contrary to probability density describing odds of locating electron in atom. In calculation of hydrogen's wave function the electron and proton constitute one entity. Hence zero OAM at ground state determined by computational and experimental means is due to OAM offset of electron and proton rotation in opposite directions at center of mass. The proton, neutron and all baryons consist of three energy levels on which the quarks are orbiting. The third energy level of 80.5Gev plays a major role in the weak force while it is filled by charged mesons that are emitted thru W boson while acquiring the level's energy. The OAM of the orbiting quarks are third or two thirds of the reduced Planck constant. The proton missing spin is resolved by the OAM of quarks. The Electron is bound state composition of a negative Pion and an Electron's neutrino. The theory predicts a neutral boson of 160Gev (Accompanied by W+ boson from 240Gev decaying particle).

The Hidden Variables Theory

2021 ◽  
Author(s):  
Israel Fried
Keyword(s):  
Wave Function ◽  
Magnetic Flux ◽  
W Boson ◽  
Energy Levels ◽  
Center Of Mass ◽  
Hidden Variables ◽  
Bound State ◽  
Electron Mass ◽  
Charged Mesons ◽  
New Variables

The book presents a new concept on several physics topics. The initial values are non-relativistic quantities of subatomic particles which the values obtained in experiments are actually their relativistic reflection. The subjects in the book are presented in such order that each new topic is based on the development of its predecessor that explains where it stems from. The book presents methods of analyzing traditional physics concepts to extract hidden embedded information that reveals new variables which are combined with those known. The new formulas yield results that match experiments accurately. It presents discoveries as: The electric charge of subatomic particle results directly from its OAM (Orbital Angular Momentum). OAM Offset exhibits neutral state. The electron mass is a magnitude that expresses quantitatively the square of its magnetic flux quantum, hence this mass in the Wave Function yields solutions that their squared values represent the flow pattern of magnetic flux surrounding electrons at energy levels, contrary to probability density describing odds of locating electron in atom. In calculation of hydrogen's wave function the electron and proton constitute one entity. Hence zero OAM at ground state determined by computational and experimental means is due to OAM offset of electron and proton rotation in opposite directions at center of mass. The proton, neutron and all baryons consist of three energy levels on which the quarks are orbiting. The third energy level of 80.5Gev plays a major role in the weak force while it is filled by charged mesons that are emitted thru W boson while acquiring the level's energy. The OAM of the orbiting quarks are third or two thirds of the reduced Planck constant. The proton missing spin is resolved by the OAM of quarks. The Electron is bound state composition of a negative Pion and an Electron's neutrino. The theory predicts a neutral boson of 160Gev (Accompanied by W+ boson from 240Gev decaying particle).

The Hidden Variables Theory

2021 ◽  
Author(s):  
Israel Fried
Keyword(s):  
Wave Function ◽  
Magnetic Flux ◽  
W Boson ◽  
Energy Levels ◽  
Center Of Mass ◽  
Hidden Variables ◽  
Bound State ◽  
Electron Mass ◽  
Charged Mesons ◽  
New Variables

The book presents a new concept on several physics topics. The initial values are non-relativistic quantities of subatomic particles which the values obtained in experiments are actually their relativistic reflection. The subjects in the book are presented in such order that each new topic is based on the development of its predecessor that explains where it stems from. The book presents methods of analyzing traditional physics concepts to extract hidden embedded information that reveals new variables which are combined with those known. The new formulas yield results that match experiments accurately. It presents discoveries as: The electric charge of subatomic particle results directly from its OAM (Orbital Angular Momentum). OAM Offset exhibits neutral state. The electron mass is a magnitude that expresses quantitatively the square of its magnetic flux quantum, hence this mass in the Wave Function yields solutions that their squared values represent the flow pattern of magnetic flux surrounding electrons at energy levels, contrary to probability density describing odds of locating electron in atom. In calculation of hydrogen's wave function the electron and proton constitute one entity. Hence zero OAM at ground state determined by computational and experimental means is due to OAM offset of electron and proton rotation in opposite directions at center of mass. The proton, neutron and all baryons consist of three energy levels on which the quarks are orbiting. The third energy level of 80.5Gev plays a major role in the weak force while it is filled by charged mesons that are emitted thru W boson while acquiring the level's energy. The OAM of the orbiting quarks are third or two thirds of the reduced Planck constant. The proton missing spin is resolved by the OAM of quarks. The Electron is bound state composition of a negative Pion and an Electron's neutrino. The theory predicts a neutral boson of 160Gev (Accompanied by W+ boson from 240Gev decaying particle).

scholarly journals Analysis of the image of pion-emitting sources in the source center-of-mass frame

2017 ◽  
Vol 53 (8) ◽  
Author(s):  
Yanyu Ren ◽  
Qichun Feng ◽  
Weining Zhang ◽  
Lei Huo ◽  
Jingbo Zhang ◽  
...  
Keyword(s):  
Center Of Mass ◽  
Mass Frame

A COMPLETE VARIATIONAL WAVE FUNCTION FOR THE GROUND STATE OF 3H AND 3He

1966 ◽  
Vol 44 (9) ◽  
pp. 2095-2110 ◽  
Author(s):  
Marcel Banville ◽  
P. D. Kunz
Keyword(s):  
Wave Function ◽  
Coordinate System ◽  
Body Wave ◽  
Center Of Mass ◽  
Minimum Energy ◽  
Equal Mass ◽  
Radial Coordinate ◽  
Orthogonal Functions ◽  
Gaussian Shape ◽  
Three Body

The three-body wave function for particles of equal mass is expanded in a systematic way by making use of a hyperspherical coordinate system. Apart from the center-of-mass coordinates, three of the variables are the usual Euler angles describing the orientation of the plane defined by the three particles. The other three variables, which describe the shape of the triangle, are represented in terms of a radial coordinate and two angular coordinates. The kinetic energy for these last three coordinates is separable and allows one to expand the three-body wave function in a complete set of orthogonal functions based upon the angular variables. The particular symmetry of the internal part of the wave function under permutations of the three particles is easily represented in terms of the set of functions for one of the angular variables. By choosing a particular set of radial functions one can then obtain the upper limit on the binding energy for the three-body system through the Rayleigh–Ritz variational procedure. The advantage of this particular coordinate system is that all but a few of the variational parameters occur linearly in the wave function, and the minimum energy can be obtained by diagonalizing a small number of the energy matrices. The method is applied to find the lower limit to a standard spin-independent potential of Gaussian shape.

scholarly journals OBSERVER INVARIANCE OF THE COLLAPSE POSTULATE OF QUANTUM MECHANICS

2012 ◽  
Vol 27 (01n03) ◽  
pp. 1345013 ◽  
Author(s):  
MILTON A. DA SILVA ◽  
ROBERTO M. SERRA ◽  
LUCAS C. CÉLERI
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Reference Frame ◽  
Relative Motion ◽  
Information Transfer ◽  
Measurement Process ◽  
Quantum Mechanical ◽  
Wave Function Collapse ◽  
Amount Of Information ◽  
Effective Efficiency

We analyze the wave function collapse as seen by two distinct observers (with identical detectors) in relative motion. Imposing that the measurement process demands information transfer from the system to the detectors, we note that although different observers will acquire different amount of information from their measurements due to correlations between spin and momentum variables, all of them will agree about the orthogonality of the outcomes, as defined by their own reference frame. So, in this sense, such a quantum mechanical postulate is observer invariant, however the effective efficiency of the measurement process differs for each observer.

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