Give expressions for computing the matrix elements Xmn of the matrix X representing the position operator X in the energy basis (using eigenvectors of the Harmiltonian operator)
Also told to consider the example of the harmonic oscillator where energy eigenvalues are En=(1/2+n)hω
The Attempt at a Solution
I'm thrown off a bit by how Xmn is defined here - if it is originally in the |x> basis, why is Xmn defined using |em> and |en>. Shouldn't these be inserted using the completeness relation to convert the matrix into the energy basis representation?