Question: Suppose that the potential jumps from zero to U 0 at x = 0 so that the free particle speeds up instead of slowing

Suppose that the potential jumps from zero to − U₀ at x = 0 so that the free particle speeds up instead of slowing down. The wave number for the incident particle is again k₁, and the total energy is 2U₀.

(a) What is the wave number for the particle in the region of positive x?

(b) Calculate the reflection coefficient R at x = 0.

(d) If one million particles with wave number k₁ are incident upon the potential step, how many particles are expected to continue along in the positive x direction? How does this compare with the classical prediction?

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