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The machinery of computing vacuum expectation values of a time-orderedsequence of position operators of the simple harmonic oscillator is alreadywell established. It rests on a Wick theorem, which enables one to decomposesuch a quantity in terms of products of \emph{pairwise contractions}, which arevacuum expectation values of a time-ordered sequence of position operatorstaken two at a time. This result naturally leads to a diagrammatic approach ofcomputing such correlators, and is already well known in the form of Feynmandiagrams. We generalise this setup to encompass expectation values of a generalordered sequence of position operators (Wightman sequences) in general densitymatrices of the simple harmonic oscillator. A Wick theorem is first developedfor this situation and consequently a diagrammatics is laid down. Wightmancorrelators in general density matrices of the \emph{anharmonic} oscillator arealso analysed and a diagrammatic formalism is developed for them too.

Diagrammatics for Wightman Correlators in General States: The Cases of the Simple Harmonic and Anharmonic Oscillators