How can the Schrodinger equation be applied to a 3D rectangular box?

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SUMMARY

The discussion focuses on applying the Schrödinger equation to a three-dimensional rectangular box, also known as the "infinite square well" in quantum mechanics. Participants suggest starting with the one-dimensional version before progressing to the three-dimensional case using Cartesian coordinates. Resources such as lecture notes and online searches for "three dimensional square well" are recommended for further understanding. The application of differential equations is emphasized as a foundational aspect of solving these problems.

PREREQUISITES
  • Understanding of the Schrödinger equation
  • Familiarity with differential equations
  • Knowledge of quantum mechanics concepts
  • Basic skills in Cartesian coordinate systems
NEXT STEPS
  • Research "three-dimensional Schrödinger equation" for detailed examples
  • Study "infinite square well" problems in quantum mechanics
  • Explore lecture notes on quantum mechanics from reputable sources
  • Practice solving differential equations related to quantum systems
USEFUL FOR

Students of quantum mechanics, physicists, and anyone interested in applying the Schrödinger equation to complex systems will benefit from this discussion.

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Can anyone give me a really simple example on how to use the eqn above to solve it?
 
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You've done the one-dimensional "particle in a box" a.k.a. "infinite square well", right? Try the three-dimensional "rectangular" version in Cartesian coordinates. A Google search for things like "three dimensional square well" or "Schrödinger equation three dimensional box" should find lecture notes about it. Maybe include the word "rectangular."
 

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