Physics – Quantum Physics
Scientific paper
2010-06-17
International Journal of Theoretical Physics (2011) 50: 1451-1467
Physics
Quantum Physics
20 pages, 8 figures, 1 table, final version
Scientific paper
10.1007/s10773-010-0654-1
In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be described in terms of classical physics without invoking violations of the energy conservation law at any time instance. A formula is presented that generates a wide class of potential barrier shapes with the desirable reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\"odinger's equation. These results, with support from numerical simulations, strongly suggest that two uncoupled classical harmonic oscillators, which initially have a 90\degree relative phase shift and then are simultaneously disturbed by the same parametric perturbation of a finite duration, manifest behavior which can be mapped to that of a single quantum particle, with classical 'range relations' analogous to the uncertainty relations of quantum physics.
No associations
LandOfFree
On Close Relationship between Classical Time-Dependent Harmonic Oscillator and Non-Relativistic Quantum Mechanics in One Dimension does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On Close Relationship between Classical Time-Dependent Harmonic Oscillator and Non-Relativistic Quantum Mechanics in One Dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Close Relationship between Classical Time-Dependent Harmonic Oscillator and Non-Relativistic Quantum Mechanics in One Dimension will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-550956