Show that the energy of a simple harmonic oscillator in the n = 1 state is 3ℏω/2 by substituting the wave function ψ1 = axe-αx2/2 directly into the schroedinger equation, as broken down in the following steps. first, calculate dψ1/dx, using a, x, and α. dψ1/dx = second, calculate d2ψ1/dx2, using a, x, and α. d2ψ1/dx2 = third, calculate α2x2ψ1 - d2ψ1/dx2, using a, x, and α. α2x2ψ1 - d2ψ1/dx2 = fourth, calculate (α2x2ψ1 - d2ψ1/dx2)/ψ1, using a, x, and α. (α2x2ψ1 - d2ψ1/dx2)/ψ1 = finally, calculate e ≡ [(α2x2ψ1 - d2ψ1/dx2)/ψ1]ℏ2/(2m), using a, x, α, m, ω, and ℏ. e ≡