Potential step, classical vs quantum mechanics

[wanderlust.xx]

Homework Statement

We have the potential step

$U(x) = 0, \ x < 0 \\ U(x) = U_0, \ x>0$

Homework Equations

&

The Attempt at a Solution

If we measure, for example, the magnitude of the transmitted current $j_T$ over the reflected current $j_R$, so

$\left| \dfrac{j_T}{j_R} \right|$

then classically we would expect no reflection for $x<0$, so we would have the reflected current as 0, whereas here if that were the case then... would this ratio be infinite?

I'm not sure if this is correct. I believe that the ratio involving the current of the incident and reflected $\left| \dfrac{j_R}{j_{inc}} \right|$ should classically be 0 since there's no reflected wave.

Just wanted to double check, really!

 

[mark726]

I would like to clarify that the ratio \left| \dfrac{j_T}{j_R} \right| is not necessarily infinite in this scenario. The behavior of the transmitted and reflected currents depends on the specific conditions of the potential step and the energy of the incident particles. In general, the ratio will vary and may not be infinite even if there is no reflected wave for x<0. It is important to analyze the potential step using the appropriate equations and consider the energy of the particles to fully understand the behavior of the transmitted and reflected currents.