a. Show that (x) = e x2/2 is an eigenfunction of A = x 2 2/x

a. Show that ψ(x) = e^−x2/2 is an eigenfunction of Aˆ = x² − ∂2/∂x²

b. Show that B̂ ψ(x), (where Bˆ = x − ∂/∂x) is another eigenfunction of Aˆ.