Help with Eigenfunctions: Find Eigenvalue-Eigenfunction Pair

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    Eigenfunctions
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Discussion Overview

The discussion revolves around finding an eigenvalue-eigenfunction pair for a specified operator, including the conditions under which the solution must be valid. The context includes mathematical reasoning related to differential operators and boundary conditions.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant requests assistance in finding a real eigenvalue-eigenfunction pair for the operator L = (\partial^2/\partialx) + (\partial/\partialx) + 2Id, under the boundary conditions u(0)=u(pi)=0.
  • Another participant encourages the original poster to share their attempts and specific difficulties to facilitate more targeted help.
  • A participant notes that since the derivatives are only with respect to x, the use of partial derivatives may not be necessary.
  • Two participants inquire about the meaning of "2Id," with one suggesting it refers to twice the identity operator.

Areas of Agreement / Disagreement

There is no consensus on the solution to the problem, and multiple interpretations of the operator and its components are present.

Contextual Notes

The discussion does not clarify the assumptions regarding the operator's properties or the implications of the boundary conditions on the eigenvalue-eigenfunction pair.

chappyform
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eigenfunctions. help!

I would be very grateful for any help on the following question:

Find any single eigenvalue-eigenfunction pair, with a real eigenvalue, for the
following operator:

[itex]\textit{L}[/itex] = ([itex]\partial^2[/itex]/[itex]\partial[/itex]x) + ([itex]\partial[/itex]/[itex]\partial[/itex]x) + 2Id

subject to the initial boundary conditions u(0)=u(pi)=0
 
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welcome to pf!

hi chappyform! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 


Since the derivatives are only with respect to x, you don't really need the partial derivatives.
 


what is 2Id?
 
X89codered89X said:
what is 2Id?

twice the identity! :wink:
 

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