 #1
Ron Burgundypants
 23
 0
 Homework Statement:
 Looking at Griffiths quantum mechanics chapter 2.1 and 2.5, how do we get to the solution to the second order differential equation?
 Relevant Equations:

(1) d^2Psi/dx^2 = k^2 Psi
(2) Psi(x) = Asin(kx) + Bcos(kx)  Ae^kx + Be^kx
(3) (1/Psi) d^2 Psi = k^2 Psi dx^2
(4) ln(Psi) d Psi = x k^2 Psi dx + c
I know the solution to the equation (1) below can be written in terms of exponential functions or sin and cos as in (2). But I can't remember exactly how to get there using separation of variables. If I separate the quotient on the left and bring a Psi across, aka separation of variables (as I was taught by physicists), and then integrate once I get (4), but then I'm still left with an operator I need to get rid of. I can of course then exponentiate away the log but then if i integrate again I'm going to get a right mess. So any ideas what to do?