- #1

Septim

- 167

- 6

## Homework Statement

In my homework assignment I have a wavefunction defined as [itex]\Psi(x)=N\exp(-|x|/a)[/itex] and I am asked to find the expectation value of momentum squared in configuration space.

## Homework Equations

[itex]\int\Psi*(x)\hat{p^2}\Psi(x)dx[/itex]

## The Attempt at a Solution

N is [itex]1/\sqrt{a}[/itex] due to the normalization requirement.The first derivative of the wavefunction is piecewise defined hence the second derivative is discontinuous at x=0. I am having difficulties in expressing the first derivative and second derivative in terms of signum function and Dirac delta function. I would like to express them as analytically as possible but due to my unfamiliarity with these functions I am unable to do so. If I disregard the discontinuity of the first derivative function at x=0 the expectation value turns out to be negative. How can I overcome this situation?

Thanks for the replies.

Edit: I have attached the original worksheet in case you would like to look at it.