Generating function for extended Jacobi polynomials, noncommutative differential calculus and the relativistic energy and momentum operators

2010 ◽  
Vol 41 (6) ◽  
pp. 969-972
Author(s):  
R. M. Mir-Kasimov
Keyword(s):  
Generating Function ◽  
Differential Calculus ◽  
Jacobi Polynomials ◽  
Relativistic Energy ◽  
Energy And Momentum ◽  
Noncommutative Differential Calculus

Energy and momentum operator substitution method derived from Schrödinger equation for light and matter waves

2019 ◽  
Vol 33 (24) ◽  
pp. 1950285
Author(s):  
Saviour Worlanyo Akuamoah ◽  
Aly R. Seadawy ◽  
Dianchen Lu
Keyword(s):  
Wave Equation ◽  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Momentum Operator ◽  
Matter Wave ◽  
Relativistic Wave Equation ◽  
Relativistic Energy ◽  
Substitution Method ◽  
Energy And Momentum

In this paper, the energy and momentum operator substitution method derived from the Schrödinger equation is used to list all possible light and matter wave equations, among which the first light wave equation and relativistic approximation equation are proposed for the first time. We expect that we will have some practical application value. The negative sign pairing of energy and momentum operators are important characteristics of this paper. Then the Klein–Gordon equation and Dirac equation are introduced. The process of deriving relativistic energy–momentum relationship by undetermined coefficient method and establishing Dirac equation are mainly introduced. Dirac’s idea of treating negative energy in relativity into positrons is also discussed. Finally, the four-dimensional space-time representation of relativistic wave equation is introduced, which is usually the main representation of quantum electrodynamics and quantum field theory.

A new formula for Jacobi polynomials

1967 ◽  
Vol 63 (4) ◽  
pp. 1045-1047
Author(s):  
B. L. Sharma
Keyword(s):  
Generating Function ◽  
Jacobi Polynomials ◽  
New Formula

The main aim of the present paper is to give a new generating function for a product of n-Jacobi polynomials. The result established in this paper is the extension of my formula (4).

A new generating function for Jacobi polynomials

1967 ◽  
Vol 63 (4) ◽  
pp. 1041-1043 ◽  
Author(s):  
B. L. Sharma
Keyword(s):  
Generating Function ◽  
Jacobi Polynomials ◽  
General Character

In this paper we give a new generating function for the Jacobi polynomials. The result obtained is of general character and includes as particular cases some of the results given earlier by Carlitz(2), Salam(1), Manocha and Sharma (3,4).

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