Understanding Eigen Functions: A Beginner's Guide

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Discussion Overview

The discussion revolves around the concept of eigenfunctions, eigenvectors, and eigenvalues, particularly in the context of differential equations and linear algebra. Participants explore the nature of these mathematical entities and their applications in various fields, including quantum mechanics and applied mathematics.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about the definitions and relationships between eigenfunctions, eigenvectors, and eigenvalues.
  • Another participant introduces the concept of eigenfunctions in the context of functional analysis and mentions that solutions to differential equations can form a vector space.
  • A link to additional resources is provided to help clarify the concepts discussed.
  • Participants acknowledge the importance of these concepts in quantum mechanics and applied mathematics.

Areas of Agreement / Disagreement

Participants generally agree on the significance of eigenfunctions and related concepts, but the initial confusion expressed by one participant indicates that there is still uncertainty and a lack of consensus on the definitions and applications.

Contextual Notes

The discussion includes references to specific mathematical concepts and their implications, but does not resolve the participant's initial confusion regarding the example provided about the function sinh(2x) and its relationship to eigenfunctions.

Who May Find This Useful

This discussion may be useful for beginners in linear algebra, functional analysis, or those interested in the mathematical foundations of quantum mechanics and applied mathematics.

Alekside
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Hello
today i learn about Eigen Function, I have many problem about Eigen Fuction

I not understand what the Eigen Fuction, Eigen Vector, Eigen Value?

For Example I not Understand this problem,
show the sinh 2x as not a Eigen Function d2/dx2, Although the equation as d2/dx2 sinh2x = 4 sinh 2x
 
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Its a concept from linear algebra, but via that wondrous subject known as functional analysis :p:p:p:p:p, and that the solutions of differential equations form a vector space, and indeed functions with rather weak crireria such as being square intergrable, also form a vector space, it is carried over to that as well:
http://tutorial.math.lamar.edu/Classes/DE/BVPEvals.aspx

Hopefully the above link will allow you to nut it out.

Its well worth your time as, not just in QM, but in applied math in general, its an EXTREMLY important copncept.

Thanks
Bill
 
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well thanks verry much bill, I will read a minute about QM, so thanks
 
Alekside said:
well thanks verry much bill, I will read a minute about QM, so thanks

No problem.

If you are still having problems do post back - on this or any issue.

It fairly easy to actually do your question, but its a lot better if you nut it out and do it.

Thanks
Bill
 

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