Is This Wave Function Normalization Correct?

[Lavace]

Homework Statement

http://www.ph.qmul.ac.uk/~phy319/problems/problems1.doc"
Question 2)b

The Attempt at a Solution

http://img685.imageshack.us/img685/9033/p270210111001.jpg

Is this correct?

Thanks!

 

[vela]

No. The parameter $\alpha$ should appear in the answer. Your set-up looks fine, though.

 

[Lavace]

No. The parameter $\alpha$ should appear in the answer. Your set-up looks fine, though.

But once we take out the infinity terms after the integral, we're left with the $\alpha$ terms, one is + and one is -, so they cancel.

What is it I'm doing wrong here?

Thanks!

 

[vela]

They can't cancel or else you'd be left with N²x0=1, which has no solution. Recheck the sign on each term.

 

[Lavace]

I can't seem to find the problem, anyone care to take a look?

The only reason I can think of is the original way I set up the integrals, and whether I add them or subtract them!

 

[vela]

$$\left[\frac{1}{-2\alpha}e^{-2\alpha x}\right]^\infty_0 \ne -\frac{1}{2\alpha}$$

 

[Lavace]

$$\left[\frac{1}{-2\alpha}e^{-2\alpha x}\right]^\infty_0 \ne -\frac{1}{2\alpha}$$

Ahhhhhh, I see now, thank you VERY much! :) Let the studying continue!