Determination of classical behaviour of the Earth for large quantum numbers using quantum guiding equation
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For quantum systems, we expect to see the classical behaviour at the limit of large quantum numbers. Hence, we apply Bohmian approach for describing the evolution of Earth around the Sun. We obtain possible trajectories of the Earth system with different initial conditions which converge to a certain stable orbit, known as the Kepler orbit, after a given time. The trajectories are resulted from the guiding equation \(p=\nabla S\) in the Bohmian mechanics, which relates the momentum of the system to the phase part of the wave function. Except at some special situations, Bohmian trajectories are not Newtonian in character. We show that the classic behaviour of the Earth can be interpreted as the consequence of the guiding equation at the limit of large quantum numbers.
KeywordsBohmian mechanics quantum trajectories correspondence principle
PACS Nos03.65.Ta 03.65.−w 03.65.Ca 04.25.−g
The authors would like to thank M Koorepaz Mahmoodabadi for his assistance and useful comments on the nonlinear equations with closed cycles which improved their ideas on the subject.
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