DESCRIPTION OF A COMPOSITE PARTICLE IN TERMS OF A FUNCTIONAL POTENTIAL WELL

1954 ◽  
Vol 32 (7) ◽  
pp. 480-491 ◽  
Author(s):  
R. Finkelstein ◽  
P. Kaus ◽  
S. G. Gasiorowicz
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Dirac Operator ◽  
Internal Wave ◽  
Composite Particle ◽  
Potential Well ◽  
Fundamental Theory ◽  
Functional Potential ◽  
Covariant Model ◽  
Relative Coordinates

A covariant two-particle wave equation of the following form is investigated:[Formula: see text]where Dk is the Dirac operator (γμpμ – im)k and F(ψ) is a functional "potential well", Ψαa. is interpreted as a probability amplitude and transforms as a spinor on both indices. ψ is the internal wave function depending only on the relative coordinates. This equation provides a covariant model which exhibits nonlocal interactions and can be studied by relatively simple methods. The investigation is primarily methodological. The physical model is similar to the Fermi–Yang pion and like it, is qualitative and not based on fundamental theory.

Molecular Orbitals and the Wave Equation

2013 ◽  
Vol 798-799 ◽  
pp. 75-78
Author(s):  
Cai Xia Xu ◽  
Zhi Ping Huang ◽  
Qi Ping Fan ◽  
Wen Yu Zhang ◽  
Hong Yi Wu ◽  
...  
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Molecular Orbital ◽  
Molecular Orbitals ◽  
Nodal Plane ◽  
Atomic Orbitals ◽  
Insight Into

A molecular orbital is the wave function for the electron, and it extends over the entire molecule. When considering the possible reactions of a molecule, molecular orbitals are required to be known. This paper gives insight into the nature of molecular orbitals and nodal plane, also explain why certain atomic orbitals “missing” in molecular orbitals.

Research on information quantization based on the quantum theory

2017 ◽  
Vol 15 (05) ◽  
pp. 1750036
Author(s):  
Feng-Ming Liu ◽  
Mei-Ling Jin
Keyword(s):  
Numerical Simulation ◽  
Information Theory ◽  
Wave Function ◽  
Wave Equation ◽  
Quantum Theory ◽  
Sample Result ◽  
Amount Of Information ◽  
The Relationship

The research on information quantization is important in the field of information theory. As a result, based on the quantum theory, the information was quantified from the information receiving aspect in this report. First of all, several concepts were presented, such as the InfoBar, the Amount of Information and the Power of Information as well as the algorithm of the Power of Information. Then, according to the relationship between the InfoBar and the amount of Information, the wave equation was decided based on the receiving information, meanwhile, the equation of wave function was defined as well. Finally, via the numerical simulation, the received model results as well as the sample result were basically matched. Thus, the validity of the model can be proved.

A note on diffraction by a right-angled wedge

1965 ◽  
Vol 61 (1) ◽  
pp. 275-278 ◽  
Author(s):  
W. E. Williams
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Surface Wave ◽  
Harmonic Wave ◽  
Boundary Value ◽  
Normal Derivative ◽  
Support Surface ◽  
Closed Form Solutions ◽  
Time Harmonic

It has been shown in recent years ((5)–(8), (10)) that it is possible to obtain closed form solutions for the time harmonic wave equation when a linear combination of the wave function and its normal derivative is prescribed on the surface of a wedge. Boundary-value problems of this type occur in the problem of diffraction by a highly conducting wedge or by a wedge whose surfaces are thinly coated with dielectric. In certain circumstances such surfaces can support surface waves and one important aspect of the solution of the boundary-value problem is the determination of the amplitude of the surface wave excited.

scholarly journals Quaternion treatment of the relativistic wave equation

1937 ◽  
Vol 162 (909) ◽  
pp. 145-154 ◽  
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Linear Functions ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Formal Representation ◽  
The Matrix ◽  
Scalar Products ◽  
Relationship Of ◽  
The Relationship

A set of matrices can be found which is isomorphic with any linear associative algebra. For the case of quaternions this was first shown by Cayley (1858), but the first formal representation was made by Peirce (1875, 1881). These were two-matrices, and the introduction of the four-row matrices of Dirac and Eddington necessitated the treatment of a wave function as a matrix of one row (as columns). Quaternions have been used by Lanczos (1929) to discuss a different form of wave equation, but here the Dirac form is discussed, the wave function being taken as a quaternion and the four-row matrices being linear functions of a quaternion. Certain advantages are claimed for quaternion methods. The absence of the distinction between outer and scalar products in the matrix notation necessitates special expedients (Eddington 1936). Every matrix is a very simple function of the fundamental Hamiltonian vectors α, β, γ , so that the result of combination is at once evident and depends only on the rules of combination of these vectors. At all stages the relationship of the different quantities to four-space is at once visible. The Dirac-Eddington matrices, the wave equation and its exact solution by Darwin, angular momentum operators, the general and Lorentz transformation, spinors and six-vectors, the current-density four-vector are treated in order to exhibit the working of this method. S and V for scalar and vector products are used. Quaternions are denoted by Clarendon type, and all vectors are in Greek letters.

CHARMONIUM SPECTRA AND DECAYS IN A SEMIRELATIVISTIC MODEL

2012 ◽  
Vol 27 (22) ◽  
pp. 1250127 ◽  
Author(s):  
BHAGHYESH ◽  
K. B. VIJAYA KUMAR
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Mass Spectra ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Model Parameters ◽  
Decay Properties ◽  
Oscillator Wave Function ◽  
Harmonic Oscillator Wave Function ◽  
Relativistic Kinetic Energy

We investigate the spectra and decays of charmonium [Formula: see text] system in a semirelativistic potential model. The Hamiltonian of our model consists of a relativistic kinetic energy term, a vector Coulomb-like potential and a scalar confining potential. From this Hamiltonian a spinless wave equation is obtained. The wave equation is then reduced to the form of a single particle Schrödinger equation. The spin dependent potentials are introduced as a perturbation. The three-dimensional harmonic oscillator wave function is employed as a trial wave function and the [Formula: see text] mass spectra is obtained by the variational method. The model parameters and the wave function that reproduce the mass spectra of the [Formula: see text] mesons are then used to investigate some of the decay properties. The results obtained are then compared with the experimental data and with the predictions of other theoretical models. We also propose possible [Formula: see text] assignments for the recently observed charmonium or charmonium-like states.

scholarly journals On the interpretation of the relativity wave equation for two electrons

1929 ◽  
Vol 124 (794) ◽  
pp. 422-425 ◽  
Keyword(s):  
Dynamical System ◽  
Wave Function ◽  
Wave Equation ◽  
Quantum Dynamics ◽  
Conjugate Function ◽  
Volume Element ◽  
Single Electron

In the general non-relativity quantum dynamics that has been developed by Dirac and others, the motion of a dynamical system is described by a wave function ψ (ξ 1 ... ξ n ; t ); and one interprets this wave function by postulating that |ψ (ξ 1 ' ξ 2 ' ... ξ n ' ; t ) | 2 d ξ 1 ' ... d ξ n ' is the probability that, at time t ξ r ' ≤ ξ r ≤ ξ r ' + d ξ r ' ( r = 1 ... n ). The relativity wave function for a single electron can be interpreted in a similar manner. If ψ( xyzt ) be the wave function, and φ the conjugate function, then φψ ( xyzt ) dx dy dz : is the probability that the electron will be found, at time t , in the volume element dx dy dz .

scholarly journals Dirac Equation in Cosmological Inertial Frame

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Dirac Equation ◽  
Inertial Frame ◽  
Gordon Equation ◽  
Probability Amplitude ◽  
Function Type ◽  
Klein Gordon ◽  
Klein Gordon Equation

Dirac equation is a one order-wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Dirac Equation from wave function, Type A in cosmological inertial frame.The Dirac equation satisfy Klein-Gordon equation in cosmological inertial frame.

scholarly journals Effects of Lorentz Symmetry Breaking and External Potential on a Relativistic Scalar Particle

2021 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Wave Function ◽  
Wave Equation ◽  
Analytical Solution ◽  
Symmetry Breaking ◽  
Scalar Potential ◽  
Scalar Particle ◽  
Lorentz Symmetry ◽  
External Potential ◽  
Energy Eigenvalues ◽  
Lorentz Symmetry Breaking

In this paper, a relativistic scalar particle under Lorentz symmetry breaking effects in the presence of a scalar potential is investigated. We introduce the scalar potential by modifying the mass via transformation M → M+S(r) in the wave equation and analyze the behaviour of a scalar particle. We see that the analytical solution to the KleinGordon equation can be achieved, and the energy eigenvalues and the wave function depends on the Lorentz symmetry breaking parameters as well as potential

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