Shooting Method Algorithm

Schroedinger's equation for the quantum wells problem is solved using the "shooting method" in which initial guesses for the wave function, Y, and its first derivative, Y', are made at the left hand boundary.  The equation is then solved left to right keeping track of the zero crossings and the divergence of the solution.   Since the value at the right hand boundary is known and the  number of zero crossings are determined by the quantum number,  the energy can be adjusted until these conditions are met and an acceptable tolerance level is reached. 

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