Reconstructing interference fringes in slit experiments by complex quantum trajectories
Article first published online: 10 JUL 2012
Copyright © 2012 Wiley Periodicals, Inc.
International Journal of Quantum Chemistry
Volume 113, Issue 9, pages 1253–1263, 5 May 2013
How to Cite
Yang, C.-D. and Su, K.-C. (2013), Reconstructing interference fringes in slit experiments by complex quantum trajectories. Int. J. Quantum Chem., 113: 1253–1263. doi: 10.1002/qua.24269
- Issue published online: 20 MAR 2013
- Article first published online: 10 JUL 2012
- Manuscript Accepted: 13 JUN 2012
- Manuscript Revised: 12 JUN 2012
- Manuscript Received: 12 FEB 2012
- two-slit experiment;
- complex quantum trajectory;
- quantum Hamilton mechanics
There are external and internal representations for a quantum state Ψ. External representation is commonly adopted in the standard quantum mechanics by exploiting probability density function Ψ*Ψ to explain the observed interference fringes in slit experiments. On the other hand, in quantum Hamilton mechanics, the quantum state Ψ has a dynamical representation that reveals the internal mechanism underlying the externally observed interference fringes. The internal representation of Ψ is described by a set of Hamilton equations of motion, by which quantum trajectories of a particle moving in Ψ can be solved. In this article, millions of complex quantum trajectory connecting slits to a screen are solved from the Hamilton equations, and the statistical distribution of their arrivals on the screen is shown to reproduce the observed interference fringes. This appears to be the first quantitative verification of the equivalence between the trajectory-based statistics and the wavefunction-based statistics on slit experiments. © 2012 Wiley Periodicals, Inc.