# Wallis meets quantum mechanics

Calculus Level 4

$\int _{ -\infty }^{ \infty }{ { e }^{ 2x(4-x) }dx={ e }^{ 8 }\prod _{ c=1 }^{ \infty }{ \frac { 2c }{ \sqrt { \alpha { c }^{ 2 }-\beta } } } }$

Find the positive, integral values of $$\alpha$$ and $$\beta$$ which satisfy the given equation. Write your answer as $$\alpha +\beta$$.

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