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For the one-dimensional potential well with finite height V 0 ( V 0  &gt; 0 or V 0  &lt; 0) the exact Green's function G is calculated by solving the differential equation. The poles of G in the complex energy plane are shown to coincide with the solutions to the Schrödinger eigenvalue equation for this potential. The well-known Green's functions for the special cases of the free particle and of the particle in an infinitely high potential box are recovered.

Exact Green's Function for the Finite Rectangular Potential Well in One Dimension