Guide me on how to go about it please

Problem 3.15 Consider the square well V ( x ) = -Vo. (a) What is the required value of the product Voa for there to be four bound states? (b) Consider a parabolic potential inscribed within the square well V(x) (see Fig. 15): Ixl > a V (x ) = \\Vo(x 2 /42 - 1 ). Ixl sa Show that the parabolic potential will have at least one odd bound state and that it cannot have more than four bound states of either parity. (c) Comment on the triangle potential V = ( Vollx/ /a - 1 ) . |x/ >a 10 V(x) V(x) -Vo Fig. 15 Parabolic well V.Problem 3.19 Consider a particle of mass on under the inuence of an attractive delta function potential 2 a V{x] = Jsn) The system is in its ground state. with energy En = 433'me and wave function\"L \"339;? 12le Since the only time dependence of this wave function comes from the phase factor e'm'". the characteristic time of the system is 1: ~ irting\". {a} In a time interval much shorter than the characteristic time of the system. the strength of the potential increases to a much larger value E: E 31. while the particle stays in the same state. What is the new ground state of the system? What are the new scattering states? {b} What is the probability of nding the system in the (new) ground state? (cl What is the probability density for nding the particle in an eigenstate of energy E :- D? What is the probability of nding the particle in any scattering state? What is its relation to the probability of pan {b}? {d} What is the energy required for the increase in strength of the potential