[latexpage] A particle is represented at time $t=0$ by the wavefunction, $$\psi(x,0)=\left{\begin{array}{cl} A(a^2-x^2),&-a\leq x \leq a\ \\0,& \mbox{otherwise}\end{array}\right.$$ Where A and a are positive real constants. The normalization constant A is: $$ A. ~~\sqrt{\frac{16}{15a^5}} ~~~B. ~~\sqrt{\frac{15}{16a^4}} ~~~C. ~~\sqrt{\frac{15}{16a^5}} ~~~D. ~~\sqrt{\frac{16}{15a^4}}$$