Consider a point particle of mass m attached to a harmonic spring with spring constant…

2. Consider a point particle of mass m attached to a harmonic spring with spring constant lc = mco20. Consider that the particle moves only in one dimension, labeled by the coordinate x, and the position of the particle at rest is at x = 0. The particle is in equilibrium at a temperature T. a) Assume that the particle behaves classically. What is the root-mean-squared fluctuation Ax .. (x2) – (x>2 of the particle about its equilibrium position (x)? b) Assume that the particle must be treated quantum mechanically. What now is Ax? (Hint: recall that for the quantum harmonic oscillator, the expected value of the kinetic energy equals the expected value of the potential energy – this is the quantum virial theorem.) c) Show that your answer in (b) reduces to your answer in (a) in the appropriate limit.

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