(a) Determine the size of the classical turning point x0 for a harmonic oscillator in its ground state with a mass of 1000 kg and a frequency of 1000 Hz. Compare your result with the size of a proton. A bar of aluminum of roughly this mass and tuned to roughly this frequency (called a Weber bar) has been used in attempts to detect gravity waves.
(b) Suppose that the bar absorbs energy in the form of a graviton and makes a transition from a state with energy En to a state with energy En+1. Show that the change in length of such a bar is given approximately by x0(2/n)1/2 for large n.
(c) To what n, on the average, is the oscillator excited by thermal energy if the bar is cooled to 1 K?