Thus, this scalar wave is not any arbitrary function.

This shows that the scalar wave and the charged particle propagate concomitantly.

We have seen that recently van Vlaenderen, 2003 [7], showed that there is a scalar wave associated with abandonment of Lorentz gauge.

Wesley and Monstein [9] claimed that the scalar wave (longitudinal electric wave) transmission has an energy density equals to 1/2[[mu].

j]), j = p, s, are finite-difference NO maps corresponding to the scalar wave equation with velocities [v.

Following [1], the rational function obtained coincides with the f-d NtD map for the PML for the scalar wave equation.

Quantum waves exist in space and are solutions of a scalar wave equation

0] is the scalar wave amplitude, frequency w = 2[pi]mc2/h, k = wave number, h = Planck's constant, m = electron mass = hw/[c.

Although the squared magnitudes of scalar wave functions are commonly identified with the irradiance of the field, the data plotted in Figs.

According to the principle of interference, the observable Poynting vector is given by the incoherent vector sum of its components in the forward and reverse components, and thus it is impermissible to express the near-zone irradiance of the field as the squared magnitudes of scalar wave functions.

According to these definitions, the diffracted field at a given point P(r,[phi]) must obey the scalar wave equation,

The Kirchhoff and Rayleigh-Sommerfeld integral equations (1) and (2) are alternative forms of the theorem of Helmholtz (5), which expresses Huygens' principle in terms of a

scalar wave function U and its normal derivatives without assuming specific attributes of this function, except that it is continuous and twice differentiable with continuous derivatives and obeys the homogeneous wave equation,