Consider a particle of mass m in the nth stationary state of the harmonic oscillator (angular frequency ω).
(a) Find the turning point, x₂.
(b) How far could you go above the turning point before the error in the linearized potential (Equation 9.33, but with the turning point at x₂) reaches 1%? That is, if

what is d?
(c) The asymptotic form of Ai(Z) is accurate to 1% as long as Z ≥ 5. For the d in part (b), determine the smallest n such that αd ≥ 5. (For any n larger than this there exists an overlap region in which the linearized potential is good to 1% and the large-z form of the Airy function is good to 1%.)

Transcribed Image Text:

V(x2 +d) - Vin(.x2 +d) V (x2) = 0.01,