A particle of mass m moving in one dimension under the potential of a harmonic oscillator has energy E = p²/2m + kox² /2

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A Particle Of Mass M Moving In One Dimension Under The Potential Of A Harmonic Oscillator Has Energy E P 2m Kox 2 1 (374.64 KiB) Viewed 25 times

A particle of mass m moving in one dimension under the potential of a harmonic oscillator has energy E = p²/2m + kox² /2. A system of N particles under the same potential, using the microcanonical ensemble, has the probability density function N N P(x₁, P₁, ..., XN, PN) = -¹8 E- 2-1 -15 (E - P²1/2m - Σ kox² /2) i=1 i=1 a) Find the joint probability density function P(x, p) for a single oscillator. b) Assuming that E = Nɛ, with & fixed, show that for large N, P(x, p) is equivalent to the Maxwell-Boltzmann distribution function. Using the result of part b), calculate: (c) the average kinetic energy for each oscillator d) the average potential energy for each oscillator.