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?
Related questions
Question
Transcribed Image Text: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 2 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?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
