Introductory QM boundary conditions

[stephen8686]

Homework Statement

A particle is represented by the following wave function:
ψ(x)=0 x<-L/2
=C(2x/L+1) -L/2<x<0
=C(-2x/L+1) 0<x<+L/2
=0 x>+L/2

use the normalization condition to find C

Homework Equations

ψ(x) must be continuous[/B]

The Attempt at a Solution

I'm supposed to say that at the points -L/2, 0, +L/2 ψ(x) must be continuous, so then I can find C. But I get C=0. For example at x= L/2 I get 0=0 and 0= -2C/L for the conditions so C=0.
I feel like I must just either overlooking something stupid or I'm just doing this completely wrong.

 

[TSny]

1But I get C=0. For example at x= L/2 I get 0=0 and 0= -2C/L for the conditions so C=0.
I feel like I must just either overlooking something stupid or I'm just doing this completely wrong.

At x = L/2 you get 0 = 0 no matter what the value of C. So, this doesn't help you determine C.

Find C by using the idea that the probability must equal 1 for finding the particle somewhere between x = -∞ and x = +∞.

 

[stephen8686]

At x = L/2 you get 0 = 0 no matter what the value of C. So, this doesn't help you determine C.

Find C by using the idea that the probability must equal 1 for finding the particle somewhere between x = -∞ and x = +∞.

Thanks TSny, I think I got it now