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The concept of partnership of potentials is studied in detail and inparticular the non-uniqueness due to the ambiguity in the election of thefactorization energy and in the choice of the solution of certain Riccatiequation. We generate new factorizations from old ones using invariance underparameter transformations. The theory is illustrated with some examples.Comment: 10 pages, LaTeX, to appear in Modern Physics Letters

THE PARTNERSHIP OF POTENTIALS IN QUANTUM MECHANICS AND SHAPE INVARIANCE