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Unbounded self-adjoint operator

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Reference no: EM13964810

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]?

Reference no: EM13964810

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