(a) A particle in a spherical box of radius b has V = 0 for 0 ( r ( b and V = ( for r > b. Use the trial function ( = b - r for 0 ( r ( b and ( = 0 for r 7 b to estimate the ground- state energy and compare with the true value h2/8mb2 (Prob. 6.2).
(b) Devise another simple variation function that obeys the boundary conditions for this problem and work out the percent error in the ground-state energy given by your function.