Eigenfunctions and operators.?

For each of the following functions determine whether the function is an eigenfunction of the d/dx and d^2/dx^2 operators, and if so determine the eigenvalues:


a) e^(-ax^2)


b) cos(bx)


c) e^(ikx) where i= sqrt (-1)

Eigenfunctions and operators.?
Let EV mean "eigenvalue"





a) For d/dx, no EV


For d^2/dx^2, no EV





b) For d/dx, no EV


For d^2/dx^2, EV = - b^2





c) For d/dx, EV = - i k


For d^2/dx^2, EV = - k^2





Let f(x) be a function, and let O(f) be an operator. If





O(f(x)) = k f(x)





Then f(x) is the eigenfunction of the operator, and k is the eigenvalue.