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a)is the function f (x) = x exp ^(-x ^ 2/2) a proper function of the...

a)is the function f (x) = x exp ^(-x ^ 2/2) a proper function of the operator d2 / dx2-x2? if so, what is the intrinsic value?
b)is the function f (x) = exp (4ix) +exp (-4ix) its own function of the operator d2 / dx2? if so, what is the intrinsic value?

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