Physical Chemistry Quantum Mechanics Wave Function Question

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1)(30 points) Suppose a system has a wave function given by
P(X) = Ax for 0 lt; x lt; L/2
P(X) = A(L-X) for L/2S X SL
P(x) =0 for x everywhere else
And subject to V(x)=0 for 0 lt; x – L/2 and V(x)=co everywhere else.
a) Draw a picture of the wave function inside a 1-dimensional box
b) Set up (do not evaluate) the integral (with the limits) you would use to determine the
normalization constant A.
c) Why do you need the wave function to be normalized?Science