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Thanks for your question!
Let us first review the Conventional Interpretation (CI) of QM: Consider an electron that is localized as a gaussian wavefunction psi(x,0) around x=0cm at t=0s. What is the probability that this electron will later be found localized as a gaussian wavefunction phi(x,10) around x= 25cm at t=10s? The CI calculates this probability by first multiplying phi*(x,10) by psi(x,10) to get the “complex transition amplitude density,” then integrating this complex transition amplitude density phi*(x,10)psi(x,10) over all space to get the complex transition amplitude A, then multiplying A by A* to get the transition probability.
In my interpretation of QM, I allow the “complex transition amplitude density” to vary with time: phi*(x,t)psi(x,t). Integrating this over all space and then multiplying the result by its complex conjugate gives exactly the same result as the CI. I interpret phi*(x,t)psi(x,t) as what is really happening between measurements.
Does this clear up your confusion?