1.) For the airy function show that you must use only to find the right boundary condition at infinity.

2.) Solve for first two even eigen function of the Schrodinger equation with regards to the corresponding energy eigenvalues. Use the first few roots listed above.

2.) Solve for first two odd eigen function of the Schrodinger equation with regards to the corresponding energy eigenvalues. Use the first few roots listed above.

d2 -1/() = / () = dz2 This is Airy's differential equation. Ai(2) {Ai(x), Bi(c)} 1.5 1 x X -10 8 -2 2 -0.5 The first few realroots of Ai (c) are approximately-2.33811 (OEIS A096714), -4.08795, -5.52056, -6.7867144, -7.94413, -9.02265, ... Similarly, the first few real roots of Bi (x) are approximately -1.17371 (OEIS A096715), -3.27109, -4.83074, -6.16985, -7.37676,-8.49195,-9.53819