Yeah nevermind, it was very trivial, just had to multiply and derivate, for some reason I thought I needed something elsePeroK said:You want to know: what is an eigenfunction?
Internet search?
An eigenfunction is a function that, when operated on by a linear operator, returns a scalar multiple of itself. In other words, the function is unchanged except for a scaling factor.
An eigenvalue is the scalar value that represents the scaling factor of an eigenfunction when operated on by a linear operator. It is often denoted by the symbol λ (lambda).
An eigenfunction proof involves finding the eigenvalues and corresponding eigenfunctions of a given linear operator. This is typically done by solving a system of equations, known as the eigenvalue problem, and verifying that the solutions satisfy the original equation.
Eigenfunctions and eigenvalues are important in many areas of mathematics and science, particularly in linear algebra and quantum mechanics. They allow us to analyze and understand the behavior of linear systems and operators, and they have applications in fields such as signal processing, image processing, and differential equations.
No, not every function has an eigenfunction. For a function to have an eigenfunction, it must satisfy certain conditions, such as being a continuous and differentiable function. Additionally, not all linear operators have eigenfunctions and eigenvalues.