Solve Harmonic Wave Equation: Manish from Germany

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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.
reedc15
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Dear Guys,

Does f(x,t)=exp[-i(ax+bt)^2] qualify as a harmonic wave? Please help!

Manish
Germany
 
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reedc15 said:
Dear Guys,

Does f(x,t)=exp[-i(ax+bt)^2] qualify as a harmonic wave? Please help!

Manish
Germany

Yes. Separate the real (cosine) and imaginary parts (sine).
 
Ok, but what about the quadratic exponent? Would my wave equation still be harmonic?
 
i actually think not, cos(x^2) or cos(2x*t) is not an harmonic wave.
in general, an harmonic function f is a function that gives f''=A*f when A is a constant. the function you gave do not fulfil this requirement.
 
Yes, cos(x^2) is not a harmonic wave, but cos[(kx+wt)^2] is, I think. "f''=A*f when A is a constant" this requirement is also fulfilled, as f comes from w, and it will take integer multiple (given by constant A)
 
I didn't understand what you mean,
d^2 f/dx^2= -f*(2xk^2+2kwt)-2k^2*sin((kx+wt)^2)
and nothing here suggest that there exist a constant A that for every t and every x
d^2 f/dx^2=Af.
 
So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks
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