I'm looking for a good website for understanding Quantum Mechanics (i.e. Time Independent Schrodinger Eq'n, Harmonic Oscillators, Rigid Rotors, etc) The operator is linear if the following is satisfied: A[c*f(x)+d*g(x)]=c*A[f(x)]+d*A[fg(x)], where A = an operator of any kind I'm having trouble coming up with cases where they are NOT equal to each other... Maybe I am doing the math incorrectly. As examples we were told to determine if the following operators were linear and if so then what their eigenvalues are: a) the first derivative operator (d/dx) b) the natural log operator (ln) c) the doubling operator (2*) Maybe my math is wrong but they all come out linear. I'm struggling with the "A[c*f(x)+d*g(x)]" portion of the equation. I've been plugging in simple equations to test their linearity and I'm simply lost. Any guidance would be greatly appreciated.