PARTICLE EQUATIONS FROM NON-ASSOCIATIVE ALGEBRAS

1959 ◽  
Vol 37 (2) ◽  
pp. 183-188
Author(s):  
Richard Bourret
Keyword(s):  
Wave Equation ◽  
Associative Algebra ◽  
Continuity Equation ◽  
Wave Equations ◽  
Relativistic Wave Equations ◽  
Lorentz Transformations ◽  
Relativistic Wave ◽  
Associative Algebras ◽  
Mass Terms

Attention is called to the neglect of linear algebras not representable by matrices in the formation and study of possible relativistic wave equations. An eight-unit non-associative algebra of Cayley is used to construct a bilocal wave equation obeying a continuity equation and possessing invariance under bilocal gauge and (proper) Lorentz transformations. Mass terms are extracted from the equations and particle and interaction interpretations are briefly discussed.

The structure of linear relativistic wave equations. I

1950 ◽  
Vol 202 (1069) ◽  
pp. 284-300 ◽  
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Total Spin ◽  
Relativistic Wave Equations ◽  
Relativistic Wave ◽  
Arithmetical Progression ◽  
Physical Requirement ◽  
Complete Determination

The structure of linear relativistic wave equations of the form ( iα µ ∂ µ - X ) ψ = 0 is discussed. In general, such equations describe particles with a spectrum of mass and spin values. It is proved that the physical requirement that all particle states can be unambiguously specified by the momentum, mass, spin and charge, leads to a complete determination of the eigenvalues of the total spin. These must form an arithmetical progression S H , S H — 1, S H — 2, ..., terminating at 0, 1/2 or 1. A coupling diagram is associated with every wave equation and necessary restrictions on the shape of the diagram are worked out. There results a useful reduction in the number of mathematical possibilities.

Bhabha relativistic wave equations

1997 ◽  
Vol 30 (11) ◽  
pp. 4005-4017 ◽  
Author(s):  
R-K Loide ◽  
I Ots ◽  
R Saar
Keyword(s):  
Wave Equations ◽  
Relativistic Wave Equations ◽  
Relativistic Wave

On relativistic wave equations

1966 ◽  
Vol 9 (4) ◽  
pp. 99-103 ◽  
Author(s):  
V. S. Tumanov
Keyword(s):  
Wave Equations ◽  
Relativistic Wave Equations ◽  
Relativistic Wave

Relativistic Wave Equations

1955 ◽  
Vol 98 (3) ◽  
pp. 801-802 ◽  
Author(s):  
Herman Feshbach
Keyword(s):  
Wave Equations ◽  
Relativistic Wave Equations ◽  
Relativistic Wave

scholarly journals l-state Solutions of the Relativistic and Non-Relativistic Wave Equations for Modified Hylleraas-Hulthen Potential Using the Nikiforov-Uvarov Quantum Formalism

2018 ◽  
Vol 3 (1) ◽  
pp. 03-09 ◽  
Author(s):  
Hitler Louis ◽  
Ita B. Iserom ◽  
Ozioma U. Akakuru ◽  
Nelson A. Nzeata-Ibe ◽  
Alexander I. Ikeuba ◽  
...  
Keyword(s):  
Wave Equations ◽  
Approximation Scheme ◽  
Jacobi Polynomials ◽  
Energy Eigenvalue ◽  
Relativistic Wave Equations ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Relativistic Wave ◽  
Type Approximation ◽  
Klein Gordon

An exact analytical and approximate solution of the relativistic and non-relativistic wave equations for central potentials has attracted enormous interest in recent years. By using the basic Nikiforov-Uvarov quantum mechanical concepts and formalism, the energy eigenvalue equations and the corresponding wave functions of the Klein–Gordon and Schrodinger equations with the interaction of Modified Hylleraas-Hulthen Potentials (MHHP) were obtained using the conventional Pekeris-type approximation scheme to the orbital centrifugal term. The corresponding unnormalized eigen functions are evaluated in terms of Jacobi polynomials.

scholarly journals Some arguments for the wave equation in Quantum theory

2021 ◽  
Vol 5 (1) ◽  
pp. 314-336
Author(s):  
Tristram de Piro ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Continuity Equation ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Atomic System ◽  
Balmer Series ◽  
Inertial Frames ◽  
The Stability

We clarify some arguments concerning Jefimenko’s equations, as a way of constructing solutions to Maxwell’s equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial frames, which is intuitively reasonable for the stability of an atomic system, and prove that the condition is equivalent to the charge and current satisfying certain relations, including the wave equations. Finally, we prove that with these relations, the energy in the electromagnetic field is quantised and displays the properties of the Balmer series.

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