Presumably, the ``Schrodinger equation" in the problem statement refers to the time-independent Schrodinger equation in one dimension, which is given by
First, we compute the second derivative of .
We plug this into the Schrodinger equation to find that
Now evaluate the above equation at to find that
Now plug this back into the Schrodinger equation.
Divide through by to find that
Hence, answer (B) is correct.