  In the one-dimensional stationary case, we construct a mechanical Lagrangian
describing the quantum motion of a non-relativistic spinless system. This
Lagrangian is written as a difference between a function $T$, which represents
the quantum generalization of the kinetic energy and which depends on the
coordinate $x$ and the temporal derivatives of $x$ up the third order, and the
classical potential $V(x)$. The Hamiltonian is then constructed and the
corresponding canonical equations are deduced. The function $T$ is first
assumed arbitrary. The development of $T$ in a power series together with the
dimensional analysis allow us to fix univocally the series coefficients by
requiring that the well-known quantum stationary Hamilton-Jacobi equation be
reproduced. As a consequence of this approach, we formulate the law of the
quantum motion representing a new version of the quantum Newton's law. We also
analytically establish the famous Bohm's relation % $\mu \dot{x} = \partial S_0
/\partial x $ % outside of the framework of the hydrodynamical approach and
show that the well-known quantum potential, although it is a part of the
kinetic term, it plays really a role of an additional potential as assumed by
Bohm.
