I have a question that's driving me insane and I'm sure there's a simple answer that I'm missing for some reason, but I'm not getting my a-ha moment. Consider 2 cases from intro QM: Infinite square well Potential barrier with E > V0 For the infinite square well, the Schrodinger eqn gives d2ψ/dx2 + k2ψ = 0 Since k2 > 0, this gives oscillating solutions (some combination of sines and cosines). Correct? For the potential barrier with E > V0, the Schrodinger eqn gives (with the potential jumping from 0 to V0 at x = 0) d2ψ/dx2 + k2IE = 0 (where kI = √2mE/(hbar2) prior to the potential step (i.e. for x < 0) and d2ψ/dx2 + k2IIE = 0 (where kII = √2m(E-V0)/(hbar2) after the potential step (for x > 0) My problem is this: As far as I can tell, both kI and kII are positive numbers (since E > V0 > 0). Why, then, do they give non-oscillating solutions? Whereas, for the infinite square well, a positive k gave oscillating solutions? Am I making a sign error here or just forgetting something from differential equations? What is different about these equations that one of them gives oscillating, and the other non-oscillating, solutions? Thanks for any help!