Integration using exponentials 2

[g.lemaitre]

Homework Statement

For this forum they use the following integration:

The Attempt at a Solution

Where does (u+a) come from? In step 2 why does the side on the left of the plus sign become zero? In step 3, how does A(0+a√π/λ) = a

This website likes you to work on problems but I can't work on something for which step 1 is a mystery.

 

[clamtrox]

Where does (u+a) come from?

They do a change of variables, x-a = u, so x= u+a

In step 2 why does the side on the left of the plus sign become zero?

The easiest way to see this is to notice that the integrand is an odd function (that is, f(-x) = -f(x)) and therefore the integral over an even interval [-n,n] is zero.

In step 3, how does A(0+a√π/λ) = a

Did they calculate the value for A before? What you are doing here is calculating an expectation value of a random variable, so it should be true that
\int_{-\infty}^\infty dx Ae^{-\lambda(x-a)^2} dx = 1

This website likes you to work on problems but I can't work on something for which step 1 is a mystery.

Yes but you can't explain every single operation you do. It just seems to me you're trying to do assignments which are a bit too difficult for you. Maybe start from something easier?

 

[g.lemaitre]

Thanks for your answers.

Yes but you can't explain every single operation you do. It just seems to me you're trying to do assignments which are a bit too difficult for you. Maybe start from something easier?

Let's say my motivation to learn math and science right now (I'm into the humanities) on a scale of 1 to 10 is about 3. I don't have the motivation to go back and learn more calculus. I just want to see how much QM I can get through with the calc I have. Then after about 2 years hopefully I'll be able to make another effort to learn math and physics with a huge burst of motivation. This time around I dedicated about 1000 hours towards math and physics, after a two year break I'll put forth another 1000 hour effort if I have the time.

 

[clamtrox]

Thanks for your answers.



Let's say my motivation to learn math and science right now (I'm into the humanities) on a scale of 1 to 10 is about 3. I don't have the motivation to go back and learn more calculus. I just want to see how much QM I can get through with the calc I have. Then after about 2 years hopefully I'll be able to make another effort to learn math and physics with a huge burst of motivation. This time around I dedicated about 1000 hours towards math and physics, after a two year break I'll put forth another 1000 hour effort if I have the time.

But it does not speed things up if you jump over things you haven't learned/have forgotten/whatever. In fact it's likely it's making your learning slower.