Jtrans T = R Jref Jine Jine (1) where Jinc, Jref, Jtrans are probability currents corresponding to the incident, reflected, and transmitted plane waves, respectively. A quantum particle of mass m and initially travelling to the +x-direction is incident to the step potential V(x) = ; 1≤0, V ;>0, where Vo > 0. Use the formulas in equation (1) to solve for the following quantities. €30 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-V F E A 2 where A and F are the incident and transmitted amplitudes, respectively.. (d) and Vo. Using the expression for T in item 2c, solve T for this potential in terms of E
Jtrans T = R Jref Jine Jine (1) where Jinc, Jref, Jtrans are probability currents corresponding to the incident, reflected, and transmitted plane waves, respectively. A quantum particle of mass m and initially travelling to the +x-direction is incident to the step potential V(x) = ; 1≤0, V ;>0, where Vo > 0. Use the formulas in equation (1) to solve for the following quantities. €30 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-V F E A 2 where A and F are the incident and transmitted amplitudes, respectively.. (d) and Vo. Using the expression for T in item 2c, solve T for this potential in terms of E
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please give detailed solutions for b to d, thank youu
Transcribed Image Text:Jtrans
T =
R
Jref
Jine
Jine
(1)
where Jinc, Jref, Jtrans are probability currents corresponding to the incident, reflected,
and transmitted plane waves, respectively.
A quantum particle of mass m and initially travelling to the +x-direction is incident to
the step potential
V(x) =
; 1≤0,
V ;>0,
where Vo > 0. Use the formulas in equation (1) to solve for the following quantities.
€30
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-V F
E A
2
where A and F are the incident and transmitted amplitudes, respectively..
(d)
and Vo.
Using the expression for T in item 2c, solve T for this potential in terms of E
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