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Proof -- swapping sum with integral

Problem In Ceperley's 95 article on path integral Monte Carlo approach I have encountered $\hat{\rho}:L^{2}(R^{3N})\to L^{2}(R^{3N})$ $\hat{\rho} = e^{-\beta \hat{H}}$, where $\hat{H}$ is a ...
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