Eigenfunction proof and eigenvalue

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SUMMARY

The discussion centers on the concept of eigenfunctions and the methods required to prove an expression as an eigenfunction. The participant initially struggled to find the necessary formulas but ultimately realized that the solution involved basic operations such as multiplication and differentiation. This highlights the importance of understanding fundamental mathematical operations in the context of eigenfunctions.

PREREQUISITES
  • Understanding of eigenfunctions and eigenvalues in linear algebra
  • Familiarity with basic calculus operations, including differentiation
  • Knowledge of mathematical proofs and their structure
  • Experience with linear transformations and their properties
NEXT STEPS
  • Study the definitions and properties of eigenfunctions and eigenvalues
  • Learn about the process of differentiation in the context of functional analysis
  • Explore linear algebra textbooks for examples of eigenfunction proofs
  • Investigate applications of eigenfunctions in quantum mechanics and differential equations
USEFUL FOR

Students and professionals in mathematics, physics, and engineering who are looking to deepen their understanding of eigenfunctions and their applications in various fields.

Andrei0408
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Homework Statement
Prove that x*e^(-x^2/2) is eigenfunction for the operator x^2 - (d^2/dx^2) and find the corresponding eigenvalue.
Relevant Equations
I don't know what equations I need to use
I searched through the courses but I can't find any formula to help me prove that the expression is an eigenfunction. Am I missing something? What are the formulas needed for this problem statement?
 
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You want to know: what is an eigenfunction?

Internet search?
 
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Likes   Reactions: Andrei0408
PeroK said:
You want to know: what is an eigenfunction?

Internet search?
Yeah nevermind, it was very trivial, just had to multiply and derivate, for some reason I thought I needed something else
 
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