The Attempt at a SolutionWhat is the Normalized Function for Y(k) = A(a-|k|)?

[Negarjf]

Homework Statement

I have to normalize the function below:
Y(k)= A (a-|k|) where |k|<=a ; And Y(k)=0 where |k|>a

Homework Equations

The Attempt at a Solution

I just get to infinity.

 

[Simon Bridge]

I just get to infinity.

... how?

Y(k)= A (a-|k|) where |k|<=a ; And Y(k)=0 where |k|>a

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

 

[Negarjf]

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

 

[Simon Bridge]

I know how does it shape...

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

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

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

 

[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.

 

[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?