A1-d nanomechanical oscillator is fabricated on a silicon microchip to have a mechanical resonance frequency of w 2t x 4.3 ghz (a) what are the energies (in ev) of the oscillator ground and first excited states? (b) compare the ground-to-first-excited-state energy difference with the ground-to-first-excited- state energy difference in the hydrogen atom. by how many times is it bigger or smaller? (c) consider the ground state wavefunction for the harmonic oscillator, derived in class. use this to show that the expectation values of the kinetic energy and potential energy operators are equal for this wavefunction. how do these relate to the ground state energy? (d) the oscillator is cooled to its ground state using the methods of laser cooing. given a mass of 31 fg (femtograms), what are the quantum mechanical uncertainties in its position and speed after the cooling if the oscillator remains in the ground state, how low must the temperature be (to avoid excitations to the first excited state)?