Originally Posted by

**joker_900** Please help, I have no idea!

Consider the set of functions {f(x)} of the real variable x defined on the interval −inf < x < inf

that go to zero faster than 1/x for x --> ħinf, i.e.

lim(x-->ħinf) xf(x) = 0

For unit weight function, determine which of the following linear operators is Hermitian when acting upon {f(x)}:

(a) d/dx + x

(b) −i d/dx + x^2

(c) ix d/dx

(d) i d3/dx3

I tried using definition of a hermitian operator as <u, Hv> = (<v, Hu>)* but I don't get what u and v are, unless they are just general members of the set {f(x)} in which case I'm still confused!