Consider a wave fucntion $$\psi(x) = 0$$ for $$x1$$ and $$\psi(x)=A(x^2-1)$$ for $$-1

Question

Consider a wave fucntion $$\psi(x) = 0$$ for $$x<-1,x>1$$ and $$\psi(x)=A(x^2-1)$$ for $$-1<x<1$$. 

1) Find the constant A from the normalization requirement.
2) Let b be an arbitrary number between -1 and 1. What is the probability that the particle is located in the range -1<x<b?

I have done the first part and got that:

$$|A|=\sqrt{\frac{15}{16|a|^2}}$$

But I'm not very sure how to do the second part?

Thanks

anonymous · Answer

I disagree with your part (a). I'm not sure where you got |a^2| in the denominator. I don't think that should be there. Maybe I'm missing something?

To find the probability between -1 and b, I would just use the same formulation, just now you have different bounds on your integral and the normalization constant is known:$$P=\int_{-1}^{b}[\sqrt{\frac{15}{16}}(x^{2}-1)]^{2}dx$$