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I must be missing something obvious but how is Tr{} defined exactly in case of contunuous spectrum operators? Everywhere I look I see it defined as a sum of [possibly infinite sequence of] eigenvalues. Is the following correct:

Given [itex]Q = \int f(q) \left| q\right\rangle \left\langle q\right| dq[/itex], where [itex]\left\langle q' | q'' \right\rangle = \delta (q'-q'')[/itex], then [itex]Tr \{\rho Q \} = \int f(q) \left\langle q | \rho | q \right\rangle dq [/itex] ?

Thanks, DK

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# Trace of operator with continuous spectrum

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