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While doing the problem of potential step, I saw that if the energy of the particle is equal to the potential energy of the step, then the wave function is a constant, or to say the probability current in the region 2 is zero ($T=0$). Does that mean that particle is reflected completely ($R=1$)?

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Yes, if $E=V_0$, then $R=1$ (https://en.wikipedia.org/wiki/Solution_of_Schrödinger_equation_for_a_step_potential#Transmission_and_reflection) as the wave vector in the high potential region $k_2=0$ (https://en.wikipedia.org/wiki/Solution_of_Schrödinger_equation_for_a_step_potential#Solution), and this does not look counter-intuitive as $R=0$ for all $E<V_0$.

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