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