Normalizing the function

1. Nov 7, 2014

Negarjf

1. The problem statement, all variables and given/known data
I have to normalize the function below:
Y(k)= A (a-|k|) where |k|<=a ; And Y(k)=0 where |k|>a

2. Relevant equations

3. The attempt at a solution

I just get to infinity.

2. Nov 7, 2014

Simon Bridge

... how?
... sketch Y vs k for the function.
What shape is it? What is the equation for the area of that shape?

3. Nov 7, 2014

Negarjf

I know how does it shape but I still don't understand how does the integral of Y^2 should be solved.

4. Nov 7, 2014

Simon Bridge

... so what is the shape? If you don't answer questions it is difficult to help you.

Show me what you are trying.
Unless I see how you are thinking I don't know how to help you.

Last edited: Nov 7, 2014
5. Nov 7, 2014

Negarjf

First one is what I got in normalizing. I can't solve the last two integrals while the fist one is infinity.
And below is what I guess the shape of the function Y(k) should be.

6. Nov 7, 2014

Simon Bridge

OK, you are starting out with: $Y(k)=A(a-|k|) : |k|<a, 0 \text{ otherwise}$

To normalize $Y$, you need to find $A: \int_{-\infty}^\infty Y^\star Y\;dk = 1$ Since Y is real, $Y^\star Y = Y^2$

In your attachment I only see you taking the range from a to +infinity.
But the wavefunction is defined over all values of k.

Note: you are mistaken about what shape the wavefunction is;
... what is the value of Y when k > a? What did you put on your sketch?