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Sunday, 30 July 2023

Towards an Einsteinian Quantum Mechanics, II: Psi from Trajectory

Here I argued for ω=vx. 
(For simplicity I work in 1+1 dimensions)

In this post I show how one can define the wavefunction of a particle from its trajectory and how it's consistent with the orthodox definitions of quantum mechanical operator. 

Let
ψ:=xi
Then dψdt=ψt=ixi1dxdt=ixixv=iψvx,
but from the above definition vx=ω,
so finally
ψt=iψω,
which is 
ˆω=it,
when expressed as an operator/eigenvalue problem. 

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