density of S(R)

[mona123]

we consider the operator A=1/_√2(∂_x+x) with domain D(A)={ u ∈ L²(R) such that Au ∈L²(R)} I am trying to solve the following question but i didn't manage to do that: Using the basic functions of Hermit and the harmonic oscillator ?(-Δ+/x/² -1)/2 = = A*A, remember why S (R) (Schwartz functions) is dense in D (A) with the norm of the graph. can you please help me.thanks in advance