- #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?