
In quaternionic physics one equation plays a major role. It is a mixture of a differential equation, a continuity equation and a coupling equation.
Φ = ∇ ψ = m φ
Here Φ, ψ and φ are continuous quaternionic distributions or more specially they are quaternionic probability amplitude distributions. ψ and φ are normalized. m acts as a coupling factor. ∇ is the quaternionic nabla. The real part of it takes the differential with respect to the progression parameter.
m follows from
m² = ∫ |Φ|² dV
Here we focus on
Φ = ∇ ψ