Show that the following pairs of wave functions are orthogonal over the indicated range. a. e x2

Show that the following pairs of wave functions are orthogonal over the indicated range.

a. e^−αx2 and x (x² − 1) e^−αx2, −∞ ≤ x < ∞, where α is a constant that is greater than zero

b. (6r /a₀ – r2 / a₀²) e^-r/3a0 and (r / a₀) e^-r/2a0 cos over the interval 0 ≤ r < ∞ 0 ≤ θ ≤ π , 0 ≤ ∅ ≤ 2π