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please provide a detailed solutions for b to d. thank you

Equation 1: Jtrans Jref T = R = Jinc Jinc (1) A quantum particle of mass m and initially travelling to the +x-direction is incident to the step potential V(x) = 0 ; x ≤0, Vo; x > 0, where Vo > 0. Use the formulas in equation (1) to solve for the following quantities. (b) (b) (c) 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.
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Transcribed Image Text:Equation 1: Jtrans Jref T = R = Jinc Jinc (1) A quantum particle of mass m and initially travelling to the +x-direction is incident to the step potential V(x) = 0 ; x ≤0, Vo; x > 0, where Vo > 0. Use the formulas in equation (1) to solve for the following quantities. (b) (b) (c) 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.
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