Schrodinger equation in a well question?

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SUMMARY

The discussion centers on solving the Schrödinger equation for a particle in a potential well, specifically applying the Wilson-Sommerfeld quantization condition. Participants emphasize the necessity of determining wave functions both inside and outside the well while adhering to boundary conditions. The mention of the particle being "classical" highlights the importance of classical mechanics principles in this quantum context. To effectively tackle the problem, users are encouraged to consult course materials and external resources, such as the provided Wilson-Sommerfeld link.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Familiarity with potential wells in quantum mechanics
  • Knowledge of boundary conditions in wave functions
  • Comprehension of the Wilson-Sommerfeld quantization condition
NEXT STEPS
  • Study the Wilson-Sommerfeld quantization condition in detail
  • Learn about boundary conditions for wave functions in quantum mechanics
  • Explore the concept of classical particles in quantum systems
  • Review examples of potential wells and their wave functions
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Students of quantum mechanics, physics educators, and anyone seeking to deepen their understanding of the Schrödinger equation and its applications in potential wells.

whitegirlandrew
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Homework Statement



(See attached picture)

Homework Equations

The Attempt at a Solution


I'm not even sure where to start :( I'm assuming that i have to find a wave function outside and inside the well and meet certain boundary conditions, but I am confused. Please help.
 

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You are supposed to apply the Wilson-Sommerfeld quantization condition.
If you don't know what that is, your first step will be to find out.
You can do this by hunting through your lecture or course notes, or searching online.
http://uw.physics.wisc.edu/~knutson/phy448/wilson-sommerfeld.pdf

Aside: what is important about the particle being classical that the author felt the need to put word "classical" in bold face? What does the "NB" note tell you to expect to happen someplace in your working?

Good luck.
 
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