چكيده
In this thesis, a new hydrodynamic formulation of complex-valued quantum mechanics is derived to reveal a novel analogy between the probability flow and the potential flow on the complex plane. For a given complex-valued wavefunction
We first define a complex potential function with and then prove that the streamline lines and the potential lines in the potential flow defined by are equivalent to the constant- probability lines and the constant-phase lines in the probability flow defined by .
The discovered analogy is very useful in visualizing the unobservable probability flow on the complex plane by analogy with the 2D potential flow on the real plane, which can be visualized by using dye streaks in a fluid laboratory.
Key words: Quantum mechanics, Complex space, Hamilton-Jacobi dynamics, Hydrodynamic formulation
