Unbounded Self Adjoint Operator.

Let H be the unbounded self-adjoint operator defined by -d^2/dx^2 (the negative of the second derivative with respect to x) on:

D(H) ={f element of L^2 | Integral( |s^2 F f(s)|^2 )ds element of L^2}

Where "F" denotes the Fourier Transform.


Question:

For the state vector h(x) =     1/sqrt(2)  if x is in [0,2]  
                                           0             if x is not in [0,2]


What is the probability that the observable H will be measured in the interval [1/2,1] ?