Discover Eigenfunctions & Eigenvalues in Triangular Quantum Well

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Discussion Overview

The discussion revolves around finding eigenfunctions and eigenvalues in a triangular quantum well, specifically involving two triangular shapes. Participants are exploring the relationship between these concepts and the Schrödinger equation.

Discussion Character

  • Exploratory
  • Technical explanation

Main Points Raised

  • One participant seeks to understand how to find eigenfunctions and eigenvalues in a triangular quantum well.
  • Another participant suggests looking up Airy Functions as a potential resource.
  • A participant reiterates the suggestion to look up Airy Functions and inquires about establishing a relationship between these functions, the triangular well, and the Schrödinger equation.
  • It is mentioned that the relationship may be described on a Wikipedia page, with a note that rescaling of variables might be necessary to align with the relevant differential equation.

Areas of Agreement / Disagreement

Participants have not reached a consensus, and multiple viewpoints regarding the approach to the problem remain. There is a suggestion to use Airy Functions, but the specifics of their application are still under discussion.

Contextual Notes

There are potential limitations regarding the assumptions needed to relate Airy Functions to the triangular quantum well and the Schrödinger equation, as well as the need for variable rescaling that has not been fully resolved.

Dirac62
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Hello all,
I need to understand how to find eigenfunctions and eigenvalues in a state of Triangular quantum well,
It would consist of two triangle.
Tnx a lot.
 
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MisterX said:
You might want to look up Airy Functions.
how can I make a relation between it and triangular well plus Schrödinger eq. in order to find eigenfunctions?
 
Dirac62 said:
how can I make a relation between it and triangular well plus Schrödinger eq. in order to find eigenfunctions?
This is described on the Wikipedia page (you may need to rescale x and y to get to the same differential equation though).
 
Thanks a lot.
 

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