Consider a particle of mass m in the nth stationary state of the harmonic oscillator (an...

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 (d) could you go above the turning point before the error in the linearized potential (Equation 8.32, but with the turning point at x2) reaches 1%? That is, if

(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 it such that ad > 5. (For any it 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%.)