Consider a particle with mass m moving in a potential U=1/2 k x², as in a mass-spring system. The total energy of the particle is E=(p² / 2 m)+1/2 k x². Assume that p and x are approximately related by the Heisenberg uncertainty principle, so p x ≈ 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?
a) Eₘin = h/4π; K/U = 1
b) Eₘin = /2; K/U = 1
c) Eₘin = h/4π; K/U = 1/2
d) Eₘin = /2; K/U = 1/2