Complex correspondence principle in the modified de Broglie-Bohm quantum mechanics

Moncy V. John

The demonstration of complex correspondence principle in a recent work is noted to have the drawback that the complex paths in the classical case and complex eigenpaths in the quantum case are very much dissimilar. Also in the de Broglie-Bohm quantum mechanics, considering the harmonic oscillator coherent states, there are marked deviations from classical correspondence. In this Letter, we demonstrate this principle by showing that the complex trajectories of classical harmonic oscillator and the complex quantum trajectories in harmonic oscillator coherent state (in a modified de Broglie-Bohm approach) are identical to each other. Such congruence, which is there even for the lowest energy states, illustrates a strong correspondence principle. It does not have the defects mentioned above and is performed without resorting to any probability axiom. The example suggests that the complex classical trajectories form the limiting case of the modified de Broglie-Bohm quantum trajectories.

http://arxiv.org/abs/1104.3197
Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph)

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