The dyadic discrete vector Green's function, [G], can be obtained through the discrete Green's function of the

scalar wave equation by applying the relationship between them.

Thus, the quaternionic Maxwell equation and continuity equation predict that there exist a

scalar wave propagating with speed of light.

He explains such key concepts as the method of moments, finite difference time domain, the finite element method, and Green's functions, with an emphasis on the analysis of the

scalar wave equation in Cartesian coordinates.

This method for the

scalar wave equation was proposed in [1] and is a combination of ideas presented in [5, 7].

j] is the

scalar wave field propagating with velocity c [[tau].

Key words: bidirectional scalar fields; boundary-value theory; circular apertures; diffraction; Kirchhoff; irradiance; near zone; optics; polarization; Rayleigh;

scalar wave functions; slits; Sommerfeld; transmission coefficients.

Then, its wave structure is easily found as a solution of the

scalar wave equation to get a quantum-wave electron that is based upon only two fundamental principles of Nature.

Professor Powers's research interests are in naval applications of optical devices, fiber optics, acousto-optic signal processing techniques,

scalar wave diffraction and acoustic imaging.

of Wisconsin-Madison) and contributors explain this critical method for solving Maxwell equations, including the one-dimensional

scalar wave equation, numerical dispersion and stability, incident wave source conditions, analytical absorbing boundary conditions, near-to-far field transformations, dispersive, nonlinear and gain materials, grids, bodies of revolution, periodic structures, antennas, photonics, advances in techniques and advances in hardware acceleration for FDTD.

Keywords: bidirectional fields; diffraction; half plane, irradiance; Kirchhoff; Maxwell; metallic screen; near zone; optics; Poynting; Rayleigh;

scalar wave functions; Sommerfeld; wave equation.

After 1945, the next step in research on wave structure was taken in 1985 when the present author, (7,8) proposed a

scalar wave equation with spherical quantum wave solutions, as a basis for the Wave Structure of Matter.

Key words: boundary value theory; circular apertures; diffraction; Kirchhoff; near zone; optics; polarization; Rayleigh; Sommerfeld;

scalar wave functions; slits.