- #1

DarkMatter5

- 39

- 5

## Homework Statement

A gaussian wave packet is given by the formula:

Ψ(x)=(1/(π

^{1/4}d

^{1/2}))e

^{ikx-(x2/2d2)}

Calculate the expectation value in this quantum state of the momentum squared.

## Homework Equations

<p

^{2}>=-ħ∫Ψ*(X) (d

^{2}Ψ(x)/dx

^{2}) dx

∫e(

^{-x2/d2}) dx= d√π

∫xe(

^{-x2/d2}) dx =0

∫x

^{2}e(

^{-x2/d2}) dx = (d

^{3}√π)/2

## The Attempt at a Solution

Here is my attempt at a solution.

I got ħ

^{2}k

^{2}. The correct answer is ħ

^{2}k

^{2}+ ħ

^{2}/(2d).

All help is very much appreciated.