122. The fact that the ground state energy (or "zero-point" energy) is not zero is a consequence of Heisenberg's indeterminacy principle. To show this, note that if a particle is bound in a one-dimensional box of size L, then Ax z L. Now carry out the following steps: (a) Using Heisenberg's inequality, what is the required indeterminacy of the momentum, Ap? (Use the correct principle AxAp > ħ/2.) (b) What is the magnitude of the momentum p of a particle in the ground state of an infinite square well? Since the particle can be moving either to the left or to the right, the uncertainty of the momentum of a particle in the ground state is Ap × 2p. (c) Compare the two values obtained for Ap. Do they agree?

122. The fact that the ground state energy (or "zero-point" energy) is not zero is a consequence of Heisenberg's indeterminacy principle. To show this, note that if a particle is bound in a one-dimensional box of size L, then Ax z L. Now carry out the following steps: (a) Using Heisenberg's inequality, what is the required indeterminacy of the momentum, Ap? (Use the correct principle AxAp > ħ/2.) (b) What is the magnitude of the momentum p of a particle in the ground state of an infinite square well? Since the particle can be moving either to the left or to the right, the uncertainty of the momentum of a particle in the ground state is Ap × 2p. (c) Compare the two values obtained for Ap. Do they agree?