Case of Eckart Potential Barrier

The solution of this equation is given in the textbook of Landau and Lifshitz [50]. With the variable changes 

The physically meaningful solution of Equation (2.34) is given by the hypergeometric function as 

In order to derive Equation (2.39), the following relation of the hypergeometric functions is used  

The transmission amplitude T and the reflection amplitude R are obtained as follows  

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