  In developing physical theories analogical reasoning has been found to be
very powerful, as attested by a number of important historical examples. An
analogy between two apparently different phenomena, once established, allows
one to transfer information and bring new concepts from one phenomenon to the
other. Here we discuss an important analogy between two widely different
physical problems, namely, the Jahn-Teller distortion in molecular physics and
the Rashba spin splitting in condensed matter physics. By exploring their
conceptual and mathematical features and by searching for the counterparts
between them, we examine the orbital texture in Jahn-Teller systems, as the
counterpart of the spin texture of the Rashba physics, and put forward a
possible way of experimentally detecting the orbital texture. Finally, we
discuss the analogy by comparing the coexistence of linear Rashba+Dresselhaus
effects and Jahn-Teller problems for specific symmetries, which allow for
non-trivial spin and orbital textures, respectively.
