How does a spinor affect a wave function?

[justpeeking]

How do spinors affect wave function solutions? Like how is the output different

 

[PeroK]

How do spinors affect wave function solutions? Like how is the output different

The wave function of a particle with spin is the composition of a spatial component and a spinor. See the Dirac equation, for example:

https://en.wikipedia.org/wiki/Dirac_equation

 

[Demystifier]

How do spinors affect wave function solutions? Like how is the output different

Due to spin, you can have a state with two electrons with the same spatial wave function. It has dramatic consequences for chemistry, see e.g. https://en.wikipedia.org/wiki/Helium_atom.

 

[pellis]

The wave function of a particle with spin is the composition of a spatial component and a spinor. See the Dirac equation, for example:

https://en.wikipedia.org/wiki/Dirac_equation

Respecting your expertise and appreciating Demystifier's enlightening answer, nevertheless might a slightly more illluminating answer* to the question be:

A spinor wave function has multiple spatial components (four for a single-electron solution of the Dirac equation).

It is the algebraic properties of this multicomponent object that makes it a spinor.

In the case of Pauli's early phenomenological theory of spin, he developed spinors that had 2-complex components (just two complex numbers). These can be combined with spatial wave functions, as your own answer states, in a manner that is very clearly illustrated in Richard Fitzpatrick's article https://farside.ph.utexas.edu/teaching/qm/lectures/node51.html

So rather than ask "How ... spinors affect wave function solutions" it might be better to ask "what characterises a wave function solution as a spinor" (i.e. being components of a spinors doesn't change (affect) the spatial wave functions themselves, but rather associates them in such a way that the whole mathematical object is - has the properties of - a spinor.)

* OK - pedantic if you prefer