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Consider a beam of particles which is incident on a potential barrier, and assume that the potential-energy function is constant in the domains of the incident and transmitted beams. The wavefunctions representing incident, reflected and transmitted particles are given by V:(1, t) = Ae (k12–wit), V.(x,t) = Be¬i(k12+wit) and V.(x,t) = Ce(ka=–-wat), respectively. a) The current density is defined by J = 2mi Calculate the incident, reflected and transmitted current densities (J;, J,, and Jt, respectively). b) Express the transmission coefficient T = |Jt/J;| and the reflection coefficient R = |Jr/J;| in terms of A, B, C, ki and k2.

Consider a beam of particles which is incident on a potential barrier, and assume that the potential-energy function is constant in the domains of the incident and transmitted beams. The wavefunctions representing incident, reflected and transmitted particles are given by V:(1, t) = Ae (k12–wit), V.(x,t) = Be¬i(k12+wit) and V.(x,t) = Ce(ka=–-wat), respectively. a) The current density is defined by J = 2mi Calculate the incident, reflected and transmitted current densities (J;, J,, and Jt, respectively). b) Express the transmission coefficient T = |Jt/J;| and the reflection coefficient R = |Jr/J;| in terms of A, B, C, ki and k2.

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Consider a beam of particles which is incident on a potential barrier, and assume that the potential-energy function is constant in the domains of the incident and transmitted beams. The wavefunctions representing incident, reflected and transmitted particles are given by V:(1, t) = Ae (k12–wit), V.(x,t) = Be¬i(k12+wit) and V.(x,t) = Ce(ka=–-wat), respectively. a) The current density is defined by J = 2mi Calculate the incident, reflected and transmitted current densities (J;, J,, and Jt, respectively). b) Express the transmission coefficient T = |Jt/J;| and the reflection coefficient R = |Jr/J;| in terms of A, B, C, ki and k2.
Transcribed Image Text:Consider a beam of particles which is incident on a potential barrier, and assume that the potential-energy function is constant in the domains of the incident and transmitted beams. The wavefunctions representing incident, reflected and transmitted particles are given by V:(1, t) = Ae (k12–wit), V.(x,t) = Be¬i(k12+wit) and V.(x,t) = Ce(ka=–-wat), respectively. a) The current density is defined by J = 2mi Calculate the incident, reflected and transmitted current densities (J;, J,, and Jt, respectively). b) Express the transmission coefficient T = |Jt/J;| and the reflection coefficient R = |Jr/J;| in terms of A, B, C, ki and k2.
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