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- 1. A particle of m moves in the attractive central potential: V(r) = ax6, where a is a constant and the normalized trial wavefunction is (r) = Ae-bx². (a) Compute the normalization constant A. (b) Calculate the ground state energy: E(b) = = (Y(x)|H|Y(x)) (4(x)|4(x)) (c) Minimize (E) to get the value of b (d) Estimate an upper bound to the energy of the lowest state4. Find the points of maximum and minimum probability density for the nth state of a particle in a one- dimensional box. Check your result for the n=2 state.3 Consider a particle, of mass m, in a box (infinite square well) with walls at x = 0 and x = a. Initially the particle had a constant wave function in the left half of the box (I e 0 to a/2). Work out the probability that energy measurement will yield the ground state energy (I e n=1, lowest energy).