A particle of mass m is located in a unidimensional potential field U (x) whose shape is shown in Fig. 6.2, where U (0) = ∞. Find:
(a) The equation defining the possible values of energy of the particle in the region E < Uo; reduce that equation to the form sin kl = ± kl √h2/2ml2Uo, where k = √2mE/h. Solving this equation by graphical means, demonstrate that the possible values of energy of the particle form a discontinuous spectrum;
(b) The minimum value of the quantity 12Uo at which the first energy level appears in the region E < Uo. At what minimum value of 12Uo does the nth level appear?