A quantum particle of mass m and initially travelling to the +x-direction is incident to the step potential V(x) = - { v ; x ≤0, Vo ; x > 0, where Vo>0. Use the formulas in equation (1) to solve for the following quantities. (b) (b) (c) 1 Solve for the scattering state wave functions for the particle in this potential. For E Vo, solve the reflection coefficient R in terms of E and Vo. Show that for E > Vo, T = E-Vo F E A where A and F are the incident and transmitted amplitudes, respectively. . Using the expression for T in item 2c, solve T for this potential in terms of E (d) and Vo. T = = Jtrans Jinc R = | Jref | Jinc (1)

A quantum particle of mass m and initially travelling to the +x-direction is incident to the step potential V(x) = - { v ; x ≤0, Vo ; x > 0, where Vo>0. Use the formulas in equation (1) to solve for the following quantities. (b) (b) (c) 1 Solve for the scattering state wave functions for the particle in this potential. For E Vo, solve the reflection coefficient R in terms of E and Vo. Show that for E > Vo, T = E-Vo F E A where A and F are the incident and transmitted amplitudes, respectively. . Using the expression for T in item 2c, solve T for this potential in terms of E (d) and Vo. T = = Jtrans Jinc R = | Jref | Jinc (1)