Consider N one-dimensional (distinguishable) classical harmonic oscillators with coordinates and moments {qi, Pi} subjec

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Consider N One Dimensional Distinguishable Classical Harmonic Oscillators With Coordinates And Moments Qi Pi Subjec 1 (376.23 KiB) Viewed 299 times

Consider N one-dimensional (distinguishable) classical harmonic oscillators with coordinates and moments {qi, Pi} subject to the Hamiltonian N 2 mo² q Pi H({q;,P;}) = Σ 2m 2 i=1 Consider a microcanonical ensemble with total energy E. a) Show that the entropy, S, can be expressed by S = k₂ lnQ NkB In 2πeΕ Nho where h is Planck's constant. b) Show that the joint probability density function of a one-dimensional harmonic oscillator can be expressed as the product of two Gaussians: 2 2 2 @ p² p(p,q) = exp mw²q² 2k T 2лk T 2mk T +