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## Homework Statement

Consider a force-free particle of mass m described, at an instant of time t = 0, by

the following wave packet:

[itex]

\begin{array}{l}

0 \ \mathrm{for} \ |x| > a + \epsilon \\

A \ \mathrm{for} \ |x| ≤ a \\

-\frac{A}{\epsilon} (x − a − \epsilon) \ \mathrm{for} \ a < x ≤ a + \epsilon \\

\frac{A}{\epsilon}(x + a + \epsilon) \ \mathrm{for} \ − a − \epsilon ≤ x < a \\

\end{array}

[/itex]

where a, ε, and a normalization constant A are all positive numbers. Calculate mean

values and variances of the position and momentum operators [itex] x , x^{2} , \sigma_{x} \ and \ p_{x}[/itex] .

## Homework Equations

[itex]

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

[/itex]

## 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:

[itex] A \ \mathrm{for} \ |x| ≤ a [/itex].

Do you have any ideas ? Thanks in advance !