Quantum Transformations

Abstract

We show that the stationary quantum Hamilton-Jacobi equation of non-relativistic 1D systems, underlying Bohmian mechanics, takes the classical form with ${\partial }_q$ replaced by ${\partial }_{\hat{q}}$ where $d\hat{q}=\frac{dq}{\sqrt{1-{\beta }^2}}$. The ${\beta }^2$ term essentially coincides with the quantum potential that, like $V-E$, turns out to be proportional to a curvature arising in projective geometry. In agreement with the recently formulated equivalence principle, these ``quantum transformations'' indicate that the classical and quantum potentials deform space geometry.

19 pages, LaTeX. Extended version to be published in Phys. Lett. A

References in corpus (3)

• A Statistical Interpretation of Space and Classical-Quantum duality
• Quantum Hamilton-Jacobi equation
• Space-wave function duality and enhanced dKdV on a Riemann surface

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