As shown in New Foundations of Physics, David Hestenes (and in other of hiw works), any complex number is a spinor (a first order spinor). When a complex number and its conjugate operate on a vector to rotate it, then the vector must rotate through 320° to return to its original position -- the identifying characteristic of a spinor.

Schrödinger's equation contains a complex number:

-h2/2m D2x2Y(x,t) + V0Y(x,t) = ih DtY(x,t)

Hence, it contains a spinor.

Physicists became aware of the nature and power of spinors when P. A. M. Dirac (x-y) used them in his quantum theory of an electron. But used a second-order spinor. And he did so -- and physicists and students and textbook writers continue this -- in a clumsy matrix form, whereas it has a simple multivector form in Clifford algebra (a.k.a multivector theory). And most of these are unaware that the complex number, which they so frequently use -- known since the Renaissance -- is a simpler form of spinor.

Had physicists and mathematicians not turned their back on Clifford algebra, the physics might have developed much sooner.