Incompatible Linearity

If both φ₁ and φ₂ obey the traditional Schrodinger equation, then φ₁+φ₂ does so.

On the other hand, if both Φ₁ and Φ₂ obey the new grammar version of Schrodinger equation, then Φ₁+Φ₂ does so.

However, when we write schematically as
Φ₁[χ] = Π_t φ₁(χ(t),t),
Φ₂[χ] = Π_t φ₂(χ(t),t),
then the above two linearities are not compatible with each other.