The Airy equation y'' = xy arises when linearising a potential near a classical turning point. Its two independent solutions are Ai(x) (decaying for x→+∞) and Bi(x) (growing for x→+∞). For x<0 both oscillate with wavelength ∝ |x|-1/4. The WKB approximation breaks down at x=0 — this is the turning point where classical mechanics says the particle stops and quantum mechanics provides the connection formulas.