The wave function for the state n = 2 of the harmonic oscillator is 2(x) = A2(2ax2

The wave function for the state n = 2 of the harmonic oscillator is ψ2(x) = A2(2ax2 – ½)e-ax2, where A2 is the normalization constant for this wave function. Show that the wave functions for the states n = 1 and n = 2 of the harmonic oscillator are orthogonal.