## Problem 7.2: Determine the energy eigenfunction for a ramped potential energy well

Please wait for the animation to completely load.

Shown are a ramped potential energy well and six trial wave functions. You may choose a trial wave function by clicking any "Trial Wave Function" link. Then you may choose a level *n* from 1 to 7 by dragging the slider to the right to increase *n*. **In the animation, ħ = 2m = 1.**

- Which Trial Wave Function(s) could represent the energy eigenfunctions of the green potential energy well?
- How do you know? Be as explicit and as complete as possible in your explanation.

This problem is inspired by one of the "best quantum mechanics problems ever posed," [D. Styer, *Quantum Mechanics: See it Now*, AAPT Kissimmee, FL Jan 2000], in reference to problem 3-17 (Exposing an unsuccessful plot, p. 152) in *An Introduction to Quantum Physics*, A. P. French and E. F. Taylor, Norton, New York (1978).

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