Eigenfunction proof and eigenvalue

[Andrei0408]

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?

 

[PeroK]

You want to know: what is an eigenfunction?

Internet search?

 

[Andrei0408]

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