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Motivated by the interest in non-relativistic quantum mechanics fordetermining exact solutions to the Schrodinger equation we give two potentialsthat are conditionally exactly solvable. The two potentials are partnerpotentials and we obtain that each linearly independent solution of theSchrodinger equation includes two hypergeometric functions. Furthermore wecalculate their reflection and transmission amplitudes. Finally we discuss someadditional properties of these potentials.

A conditionally exactly solvable generalization of the potential step