Thread: why this expression means all solutions

http://i45.tinypic.com/140hqtx.jpg

they say that the integral represents all the solutions for the equation


i cant understand why???

as i see it we can multiply our found single solution and multiply it by a constant
and we get endless variations of our single solution.

Originally Posted by transgalactic

http://i45.tinypic.com/140hqtx.jpg

they say that the integral represents all the solutions for the equation


i cant understand why???

as i see it we can multiply our found single solution and multiply it by a constant
and we get endless variations of our single solution.

Well, this can be attained by A(k), which is any arbitrary (integrable) function of k...

Tonio

Originally Posted by tonio

Well, this can be attained by A(k), which is any arbitrary (integrable) function of k...

Tonio

i cant see how it cant be attained by the properties of A(k)

i dont know whats A(k)
i dont know why they take the integral

if i would be asked to find all the varieties of the single solution
i would just multiply it by constant

i dont know what they have done there

Originally Posted by transgalactic

i cant see how it cant be attained by the properties of A(k)

i dont know whats A(k)
i dont know why they take the integral

if i would be asked to find all the varieties of the single solution
i would just multiply it by constant

i dont know what they have done there

]

A(k) is ANY complex (integrable) function, so if you want to multiply soem particular solution by s, say, you can as well take sA(k) since A(k) is pretty arbitrary...

Tonio

ok so A(k) is like multiplying by constant
it creates a variety of solutions which differ by the multiplication of this function
depending on the k we put inside



whats the integral for?

integral means sum for me
why they sum all the solutions?

of course k needs to go from plus infinity till minus infinity

but why sum all the solutions??