Wave packet: math question. QT(Bohm's book)

[knockout_artist]

Hello,

In David Bohm,s Quantum Theory, in chapter 3 section 2(motion of pulse of light)
There is this equation, I could not understand how, integrating LHS produced a sin.

Please help.

note:
LHS: k₀ +Δk is super script. I did not know how to put it closer to integration sign.

E_x(x)= ∫_k0-Δk ^k₀+Δk dke^ik(x-x₀) = 2 ((sin Δk (x-x₀)) / (x-x₀)) e^{ik₀(x-x₀)}

 

[Nugatory]

There is this equation, I could not understand how, integrating LHS produced a sin.

If you could show us how far you did get, we will be better able to help you.

 

[knockout_artist]

Well.. only thing close enough I could think of was (e^ik - e^ik)/2
would make is sin on right hand side.
Then also e^{ik₀(x-x₀)} would also get carried on on the RHS.

 

[Nugatory]

Well.. only thing close enough I could think of was (e^ik - e^ik)/2
would make is sin on right hand side.

Look at the bounds of the definite integral.

 

[knockout_artist]

I think I have to look at my calculus book.
I will post if I still have problem.

Thanks for looking at it.