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Homework Statement
The vector p> is given by the function x+2x^{2} and the operator A = 1/x * d/dx, with x = [0,1].
a) Compute the norm of p>
b) Compute Ap>. Does Ap> belong to the VS of all real valued, continuous functions on the interval x = [0,1]?
c) Find the eigenvalues and eigenvectors of A.
Homework Equations

The Attempt at a Solution
a) For the norm, I have that it should be [tex]\sqrt{<pp>}[/tex] but I don't know how to find the scalar product of x+2x^{2} with itself
b) Ap> is just 1/x + 4, which isn't continuous at x=0 so no?
c) I have no idea how to turn the operator into a matrix. Once I have the matrix, it should be easy but what is the matrix form of A = 1/x * d/dx? Or do I need to use the eigenvalue equation and say that Ap> = eigenvaluep>?
Any help would be appreciated.
Thanks!
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