## GR0877 Problem 89

**PROBLEM STATEMENT**: *This problem is still being typed*.

**SOLUTION**: (**D**) The reflection coefficient is defined in terms of the incident and reflected probability current density : , where and . Thus, . According to the standard boundary conditions, is always continues and is continues (except at points where the potential becomes infinite). Therefore, for the point one has for continuity of and for continuity of . From these two equations and .

*Found a typo? Comment!*

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Fastest way to solve this one is by observing the limit as k2->k1 (such that the added potential step gets smaller). You can see that only (D) has the limit of R=0.

You may also notice that from Fresnel’s equations (d) is by definition the reflection coeffiecent.

I believe there is a typo in that the first derivative continuity should give k_1A-k_1B=k_2C since the reflected and incident waves have the same wavenumber in this problem.