How to determine a Limits of Integration of Wave Packet

[Zaknife]

Homework Statement

Consider a force-free particle of mass m described, at an instant of time t = 0, by
the following wave packet:
<br /> \begin{array}{l}<br /> 0 \ \mathrm{for} \ |x| &gt; a + \epsilon \\<br /> A \ \mathrm{for} \ |x| ≤ a \\<br /> -\frac{A}{\epsilon} (x − a − \epsilon) \ \mathrm{for} \ a &lt; x ≤ a + \epsilon \\<br /> \frac{A}{\epsilon}(x + a + \epsilon) \ \mathrm{for} \ − a − \epsilon ≤ x &lt; a \\<br /> \end{array}<br />
where a, ε, and a normalization constant A are all positive numbers. Calculate mean
values and variances of the position and momentum operators x , x^{2} , \sigma_{x} \ and \ p_{x} .

Homework Equations

<br /> 1=\int_{-\infty}^{\infty} |\psi(x,t)|^{2}<br />

The Attempt at a Solution

I want to determine normalization constant A. I don't know what kind of integration limits i should use for the case:
A \ \mathrm{for} \ |x| ≤ a.
Do you have any ideas ? Thanks in advance !

 

[dextercioby]

You have a lot of intervals and need to use the fact that the integral will be a sum of integrals for each interval. So write all the integrals, compute them all the find A. Then compute all other items.

 

[Zaknife]

Ok , so far i have:
\int_{??}^{??} A^{2} dx (?) -\frac{A^{2}}{\epsilon^{2}}\int_{a}^{a+\epsilon} (x-a-\epsilon)^{2} dx +\frac{A^{2}}{\epsilon^{2}}\int_{-a-\epsilon}^{a} (x+a+\epsilon)^{2} dx =1. My question is what are the integration limits for the first integral ?

 

[dextercioby]

Where did you pick the first one from ? Is there an interval where the wavefunction is 1 ?

 

[Zaknife]

So, should i include first integral ? That was my problem/question ?