We explore the quantum aspects of an elastic bar supported at both ends and subject to compression. If strain rather than stress is held fixed, the system remains stable beyond the buckling instability, supporting two potential minima. The classical equilibrium transverse displacement is analogous to a Ginsburg-Landau order parameter, with strain playing the role of temperature. We calculate the quantum fluctuations about the classical value as a function of strain. Excitation energies and quantum fluctuation amplitudes are compared for silicon beams and carbon nanotubes.PACS numbers: 03.65.-w, 62.25.+g, 46.32.+x, 05.40.-a The continuing drive towards semiconductor device miniaturization and integration has resulted in fabrication and micromachining technologies that are capable of producing artificial structures with features approaching the ten nanometer length scale. To go beyond this scale, naturally occurring and chemically organized structures are receiving much attention. The availability of these top-down and bottom-up nanofabrication capabilities has initiated the new area of nanomechanics [1,2,3,4,5] in which ultra small mechanical systems are used to explore both fundamental and applied phenomena. Recently, two reports have appeared on two-state nanomechanical systems. In one [6], crossed carbon nanotubes were suspended between supports and the suspended element was electrostatically flexed between two states. In the second [7], it was proposed to use an electrostatically flexed cantilever to explore the possibility of tunneling in a nanomechanical system.In this Letter we discuss quantum effects in a two-state mechanical system that has a tunable, symmetric potential function. This mechanical system has analogies to the superconducting interference device in which the first observation of a coherent superposition of macroscopically distinct states was recently reported [8]. Specifically, we consider a suspended elastic bar under longitudinal compression. The compression is used to adjust the potential energy for transverse displacements from the harmonic to the double-well regime, as shown in Fig. 1, with strain playing a role analogous to temperature in a Ginzburg-Landau system. As the compressional strain is increased to the buckling instability [9], the frequency of the fundamental vibrational mode drops continuously to zero. By controlling the separation between the ends of the bar, i.e. fixing the strain, the system remains stable beyond the instability and develops a double well potential for the transverse motion. Since both the well depth and asymmetry are tunable, a variety of quantum phenomena may be explored, including zero-point fluctuations, tunneling, and coherent superpositions of macroscopically distinct states. In the latter two cases, the system may provide a mechanical realization (at least in theory) of models studied in Refs.[10] and [11], respectively. We have applied the model to suspended silicon beams and carbon nanotubes, and show that in both cases the quantum fluctuatio...