- #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.