I was trying to learn Quantum physics by myself using MIT's 8.04 course. I came accross this equation:
I don't understand why the above is true. I understand the definition of linearity. But I don't know why two solutions to the above wouldn't be a solution if both sides involve derivatives (I am fully aware that one is a derivative wrt x and the other to t, but I don't know why that matters).
I don't understand why the above is not a linear equation and why adding/multiplying solutions doesn't work. Can someone give me an example?