A. Bouda
Published 2000-04-10, updated 2000-12-12Version 3
A unified form for real and complex wave functions is proposed for the stationary case, and the quantum Hamilton-Jacobi equation is derived in the three-dimensional space. The difficulties which appear in Bohm's theory like the vanishing value of the conjugate momentum in the real wave function case are surmounted. In one dimension, a new form of the general solution of the quantum Hamilton-Jacobi equation leading straightforwardly to the general form of the Schr\"odinger wave function is proposed. For unbound states, it is shown that the invariance of the reduced action under a dilatation plus a rotation of the wave function in the complex space implies that microstates do not appear. For bound states, it is shown that some freedom subsists and gives rise to the manifestation of microstates not detected by the Schr\"odinger wave function.
Comments: 15 pages, LateX, no figures, substantially revised with an additional section about microstates, accepted for publication in Foundation of Physics Letters
Journal: Found.Phys.Lett. 14 (2001) 17
Differences between the trajectory representation and Copenhagen regarding the past and present in quantum theory
Classical Limit of the Trajectory Representation of Quantum Mechanics, Loss of Information and Residual Indeterminacy
Quantization of a one-dimensional system by means of the quantum Hamilton-Jacobi equation
