Eigenvalue5

Wave Function Exercise #3

Please answer the  following 2 questions regarding the Physlet:

 Choose a Wave Function, then a Level:  
Trial Wave Function A Trial Wave Function D
Trial Wave Function B Trial Wave Function E
Trial Wave Function C Trial Wave Function F

Description

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 using the slider.   Two questions further test the understanding of the relationship between the wave function and the potential energy. 

Questions

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

  2. How do you know?  Be as explicit and as complete as possible in your explanation.

References

 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 and http://www.oberlin.edu/physics/dstyer/TeachQM/see.html.], Problem 3-17 (Exposing an unsuccessful plot, p. 152) in An Introduction to Quantum Physics, A. P. French and Edwin F. Taylor, Norton, New York, 1978. 

Credits

Script by Mario Belloni and Wolfgang Christian.
Questions by Mario Belloni and Larry Cain.
Java applets by Wolfgang Christian.