Consider the square of the derivative operator D^2
(a) Show that D^2 is a linear operator
(b) Find the eigenfunctions and corresponding eigenvalues of D^2.
(c) Give an example of an eigenfunction of D^2 which is not an eigenfunction of D.
D is a linear operator. If f and g are two functions and a and b two complex numbers, then:
D[a f + b g] = a D[f] + b D[g] (1)
Which is the defining property of a linear operator (or equivalent to other set of defining properties)
The operator D^2 is defined as:
D^2f = ...
A detailed solution is given. The expert considers the square of the derivative operators and linear operators.