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# Chapter 10: The Infinite Square Well

The infinite square well is the prototype bound-state quantum-mechanical problem. Despite this being a *standard* problem, there are still many interesting subtleties of this model for the student to discover. Our understanding of this problem, whether it be in regards to energy eigenfunctions in position or momentum space, time evolution, or the dynamics of wave packets, will be useful for the study of more realistic problems.

# Table of Contents

## Sections

- Section 10.1: Classical Particles and Wave Packets in an Infinite Well.
- Section 10.2: The Quantum-mechanical Infinite Square Well.
- Section 10.3: Exploring Changing Well Width.
- Section 10.4: Time Evolution.
- Section 10.5: Classical and Quantum-mechanical Probabilities
- Section 10.6: Two-state Superpositions.
- Section 10.7: Wave Packet Dynamics.
- Section 10.8: Exploring Wave Packet Revivals with Classical Analogies.

## Problems

- Problem 10.1: Compare classical and quantum infinite square well probability distributions.
- Problem 10.2: Rank infinite square well energy eigenfunctions
- Problem 10.3: Determine the expectation values for the energy eigenfunction.
- Problem 10.4: Determine the time-independent expectation values for a two-state superposition.
- Problem 10.5: Determine the time evolution of Δ
*x*and Δ*p*for a two-state superposition. - Problem 10.6: Determine the components of a superposition.

## Alternate Visualizations

- Section 10.4: Time Evolution.
- Section 10.5: Classical and Quantum-mechanical Probabilities
- Section 10.6: Two-state Superpositions.
- Section 10.7: Wave Packet Dynamics.
- Problem 10.5: Determine the time evolution of Δ
*x*and Δ*p*for a two-state superposition.