The function f(x,t)=exp[-i(ax+bt)^2 does not qualify as a harmonic wave due to its quadratic exponent, which fails to meet the harmonic function requirement of f''=A*f, where A is a constant. While separating the real and imaginary parts can yield cosine and sine components, the presence of the quadratic term complicates its classification. Discussions highlight that functions like cos(x^2) are not harmonic, while cos[(kx+wt)^2] is considered harmonic. The mathematical analysis reveals that the second derivative does not conform to the necessary form to establish a constant A. Therefore, the consensus is that the original function does not represent a harmonic wave.
