The physical interpretation of wave mechanics. I

Quantization from an exponential distribution of infinitesimal action

“…It also provides the basis for the development of interpretation of quantum theory in term of traditional classical statistical mechanics. These include the hydrodynamics interpretation [1,[19][20][21][22][23][24][25] and Bohmian mechanics [26][27][28][29][30][31]. Let us note however that the idea that the velocity of the particle is determined by the phase of a quantum wave in Bohmian mechanics is firstly developed by de Broglie as early as 1923.…”

Statistical origin of quantum mechanics

“…The first one is the evolution equation for ρ and is a continuity equation while the second is the evolution equation for S and can be viewed as an Euler equation or as an Hamilton-Jacobi equation with an extra contribution to the energy corresponding to the presence of the quantum potential. The quantum fluid obtained in this way starting from the Schrödinger equation was studied extensively by various authors [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Takabayashi has shown that the quantum potential leads to a particular form for the stress tensor of the quantum fluid [5].…”