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Quantum Mechanics and Particle Incident

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Part 1
A particle incident on the potential step with
a certain energy E < U is described by the
wave ψ(x) = (1/ 2)* {(1 + i)e^ikx + (1 − i)e^ikx }, x ≤ 0
ψ(x) = e ^−kx , x ≥ 0
Evaluate the penetration depth δ = 1/k for
9.4 MeV protons incident on this 23.4 MeV
step. Answer in units of fm.

Part 2
A particle of energy E approaches a step bar-
rier of height U0 .
What should be the ratio E/U0 so that the
reflection coefficient is 0.2?

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Solution Preview

Hi there

Here is the solution to the two questions.

Note that for the second problem I used the ...

Solution Summary

This solution contains step-by-step calculations to determine the penetration depth and the ratio of E/U0 for a specific reflection coefficient.