QUESTION 3 (20 MKS) a) Obtain the time-independent Schrodinger Wave equation from the time dependent equation....

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QUESTION 3 (20 MKS) a) Obtain the time-independent Schrodinger Wave equation from the time dependent equation. [10 mks] b) Solve the time-independent Schrodinger equation given that,(x) = Aekx [10 mks] QUESTION 4 (20 MKS) a) Show that the quantum expression for the kinetic energy of free particle bound in a 1 D box of width L is given as, E nh 8mL [10 mks] b) Calculate the expected values for momentum , for a particle in an infinite square well of width defined by 0 < x < L, for n = 1, given the applicable wave function in the well as: (x) = [2] sin [*] QUESTION 5 (20 MKS) Consider a square well whose the potential regions for the model can be represented as follows, V(x) { Region I V(x) Vo x <0 or x>L Regions I & III 0 < x Vo) [10 mks] ii) Solve the Schrodinger equation for this particle in (E < Vo) [10 mks] QUESTION 3 (20 MKS) a) Obtain the time-independent Schrodinger Wave equation from the time dependent equation. [10 mks] b) Solve the time-independent Schrodinger equation given that,(x) = Aekx [10 mks] QUESTION 4 (20 MKS) a) Show that the quantum expression for the kinetic energy of free particle bound in a 1 D box of width L is given as, E nh 8mL [10 mks] b) Calculate the expected values for momentum , for a particle in an infinite square well of width defined by 0 < x < L, for n = 1, given the applicable wave function in the well as: (x) = [2] sin [*] QUESTION 5 (20 MKS) Consider a square well whose the potential regions for the model can be represented as follows, V(x) { Region I V(x) Vo x <0 or x>L Regions I & III 0 < x Vo) [10 mks] ii) Solve the Schrodinger equation for this particle in (E < Vo) [10 mks]