The elementary concept of conformal mappings, briefly reviewed in
the Appendix, appears here merely as a motivation of a very routine
change of variables (16) in an exactly solvable ordinary
differential Schroedinger equation. This concept does not seem to be
too much related to the subject of the paper itself, offering an
exercise-like description of several well known facts about
transition from a Casimir of su(1,1) and from its
differential-operator representation to a solvable bound-state
problem in Quantum Mechanics.
MR2485574 Yahiaoui, S.-A.; Bentaiba, M. A group-theoretical method
for Natanzon potentials in position-dependent mass background by
means of conformal mappings. Internat. J. Theoret. Phys. 48 (2009),
no. 2, 315--322. 81Qxx (33C90)