Zero-Point Energy Consider a particle with mass m moving in a potential U = kx2, as

Zero-Point Energy Consider a particle with mass m moving in a potential U = ½ kx2, as in a mass-spring system. The total energy of the particle is E = p2/2m + ½ kx2. Assume that p and x are approximately related by the Heisenberg uncertainty principle, px ≈ h.
(a) Calculate the minimum possible value of the energy E, and the value of x that gives this minimum E. This lowest possible energy, which is not zero, is called the zero-point energy.
(b) For the x calculated in part (a), what is the ratio of the kinetic to the potential energy of the particle?