1. Families of finite square wells. A particle of mass m has N quantized energy levels in a one-dimensional square well of depth V_0 and width L. N is more than 10

a) Approximately how many bound states does the particle have in a well of the same depth but width 2L?

b) Approximately how many states does the particle have in a width L but depth 2V_0?

c) Approximately how many states does the particle have in a depth 2V_0 and width 2L?

d) How many bound states does the particle have in a well of depth V_0 / 4 and width 2L? In a well of depth 4V_0 and width L/2?