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

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

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genius_generous answered 1 year ago

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