Equivalence principle, Planck length and quantum Hamilton–Jacobi equation

The Quantum Stationary HJ Equation (QSHJE) that we derived from the equivalence principle, gives rise to initial conditions which cannot be seen in the Schrödinger equation. Existence of the classical limit leads to a dependence of the integration constant ℓ=ℓ1+iℓ2 on the Planck length. Solutions of the QSHJE provide a trajectory representation of quantum mechanics which, unlike Bohmʹs theory, has a non-trivial action even for bound states and no wave guide is present. The quantum potential turns out to be an intrinsic potential energy of the particle which, similarly to the relativistic rest energy, is never vanishing.