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Transmission coefficients of a 1D particle in delta potentia

(See attached file for full problem description)

4. A particle of mass m, with energy E>0, is moving in the potential

V(x) = g

a. Write down the solution of the Schrodinger equation in all three regions (x<a,
-a<x<a, x>a) for this situation. Assume that the particle is incident from the left.
b. Write down the appropriate continuity conditions at x = +a and x = -a.
c. Compute the transmission coefficient. Please express your final answer in terms of p*a/h-bar, where p = , and the constant


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The calcuations with fully detailed explanations are in the attached file ...