wave equation

…normal mode solutions of the wave equation are superposed, the result is a solution of the form where the coefficients a₁, a₂, a₃, … are arbitrary constants. Euler did not state whether the series should be finite or infinite; but it eventually turned out that infinite series held the key…

…that he arrived at a wave equation, according to which transverse electric and magnetic disturbances were propagated with a velocity that could be calculated from electrical measurements. These measurements were available to Maxwell, having been made in 1856 by the German physicists Rudolph Hermann Arndt Kohlrausch and Wilhelm Eduard Weber,…

…described mathematically by the general equation for wave motion, which is written in simplified form as:

The wave equation, in particular, is exceedingly important. Waves arise not only in musical instruments but in all sources of sound and in light. Euler found a three-dimensional version of the wave equation, which he applied to sound waves; it takes the form w_tt = c²(w_xx…

…in the solutions of the wave equation the postulates of Bohr but went much further. Bohr’s theory had come to grief when even two electrons, as in the helium atom, had to be considered together, but the new quantum mechanics encountered no problems in formulating the equations for two or…