How to solve Time-independent Schrodinger Equation (with Shooting Method)

Shooting Method, somtimes we call this 'Wag the dog method'

We'll draw the solution of Schrodinger equation with Mathematica

 

K = 0.9, u[0]=1, u'[0]=0

K = 5.0001

K = 6.9

K = 6.9999