I would appreciate if someone could set me straight here. I understand if I have an arbitrary operator, I can express it in matrix component notation as follows:(adsbygoogle = window.adsbygoogle || []).push({});

Oi,j = <vi|O|vj>

Is it possible to get a representation of the operator O back from this component form. I'm more interested in what to do in the case of continuous i and j so I assume I will have to do a 2 dimensional integral. Also how could I go from this form to calculate an expectation value <O>. Again I would have thought this would be a 2D integral as-well but something a bit more as I would want this <X|O|X> where X is a wave-function.

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# Help with Operators written as components.

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