A potential well of previous problem is called shallow if its depth satisfies the condition U < < < ma2 (1) We already know that no matter how shallow the well is, in one dimension it always hosts a bound state. (a) Derive the approximate expression for the energy of this state and compare its magnitude to the depth of the well Uo- (b) Derive the approximation expression for the normalized wave function y(x) of this state. (c) Determine the probability to find the particle inside the well, comment on how it compares to unity and explain you result. (d) Determine the average potential and kinetic energies of the particle in this state. (e) At this point you should notice that there exists a great deal of similarity between the properties of this shallow state and a bound state of a particle in the delta-function potential well discussed in Problem 4 of the previous assignment. Explain how your shallow well bound state results map onto those of a particle in a delta-function potential well U(x) = -ad(x) specifically commenting on what happens to the condition (1). (2)