Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-01-09
Phys.Lett.A249:180-190,1998
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, LaTeX. Extended version to be published in Phys. Lett. A
Scientific paper
10.1016/S0375-9601(98)00723-3
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 $d\hat q={dq\over \sqrt{1-\beta^2}}$. 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.
Faraggi Alon E.
Matone Marco
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