Is Classical Velocity Potential a Quantum Mechanical Wavefunction?

Abstract

Quantum mechanics is a theoretical formalism that is completely different from classical particle kinematics (classical mechanics). In general, classical kinematics is identified as a macroscopically approximate formalism of quantum mechanics. In this paper, however, we attempt to seek the origin of quantum mechanical wavefunction in classical mechanics. In our prescription, a classical velocity potential can be introduced for a moving particle, i.e., since the curl of a classical particle velocity vanishes, the classical momentum can be expressed as a gradient of a certain function (related to the so-called classical velocity potential). It can be found that this velocity potential can serve as a quantum mechanical wavefunction. A classical particle is always accompanied by such a velocity potential. Such a prescription will be employed to three cases: two-particle direct product state, single-particle superposition state, and entangled states (superposition of direct product states). We show that the classical particle momentum can also be in a state of superposition with the wavefunction as its weight coefficients.
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