strings235
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hey does anyone know if studying Fourier analysis is going to aid in physics, particularly in string theory or quantum physics?
Will studying fourier analysis prepare one for string theory and QP?
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Yes it is.
Just one quick example: often physicists have to solve differential equations, like [tex]\mathcal{L}\phi = f[/tex] for given [tex]f[/tex] and differential operator [tex]\mathcal{L}[/tex]. One way do do this is by constructing a Greens function which satisfies [tex]\mathcal{L}G(x) = \delta(x)[/tex] (that's a Dirac delta) and then the equation can be solved for any [tex]f[/tex] by convolution; [tex]\phi = G * f = \int G(x - x') f(x') dx'[/tex]. Once you do this for different differential operators, you'll notice that it's often much handier to solve the Fourier components of [tex]G[/tex] separately (especially since the delta function has such an easy Fourier transform) and then back-transform them to get G.
In fact, I have heard that in field theories (QFT, for example) people love working in Fourier space, as problems are often relatively simple there and a real pain in the neck to do in real space.
So my advise would be: if you can study Fourier analysis, do it.
Just one quick example: often physicists have to solve differential equations, like [tex]\mathcal{L}\phi = f[/tex] for given [tex]f[/tex] and differential operator [tex]\mathcal{L}[/tex]. One way do do this is by constructing a Greens function which satisfies [tex]\mathcal{L}G(x) = \delta(x)[/tex] (that's a Dirac delta) and then the equation can be solved for any [tex]f[/tex] by convolution; [tex]\phi = G * f = \int G(x - x') f(x') dx'[/tex]. Once you do this for different differential operators, you'll notice that it's often much handier to solve the Fourier components of [tex]G[/tex] separately (especially since the delta function has such an easy Fourier transform) and then back-transform them to get G.
In fact, I have heard that in field theories (QFT, for example) people love working in Fourier space, as problems are often relatively simple there and a real pain in the neck to do in real space.
So my advise would be: if you can study Fourier analysis, do it.
strings235
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and would you recommend I study applied or theoretical mathematics if i were to do a double major with physics? thanks for the post btw.
Reverie
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strings235 said:
I would recommend studying theoretical mathematics. Differential Geometry and Functional Analysis would be quite useful. Fourier Analysis is also quite useful. Many, many things are quite useful...
[tex]E=mc^{2}[/tex]
