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

 Choose a Wave Function, then a Level:

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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 nIn the animation, ħ = 2m = 1.

  1. Which Trial Wave Function(s) could represent the energy eigenfunctions of the green potential energy well?
  2. 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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