A particle of mass m is trapped in a potential well which has the form, V = 1/2mω2x2. Use the variation method with the normalized trial function (1/√a)cos(πx/2a) in the limits −a < x < a, to find the best value of a.
The best approximation to the ground-state wave function is obtained by setting ∂E/∂α = 0. This gives
