The partnership of potentials in Quantum Mechanics and Shape Invariance
  The concept of partnership of potentials is studied in detail and in particular the non-uniqueness due to the ambiguity in the election of the factorization energy and in the choice of the solution of certain Riccati equation. We generate new factorizations from old ones using invariance under parameter transformations. The theory is illustrated with some examples. 
Jose F. Carinena and Arturo Ramos