Reconstructing interference fringes in slit experiments by complex quantum trajectories

Abstract

There are external and internal representations for a quantum state W. External representation is commonly adopted in the standard quantum mechanics by exploiting probability density function W*W to explain the observed interference fringes in slit experiments. On the other hand, in quantum Hamilton mechanics, the quantum state W has a dynamical representation that reveals the internal mechanism underlying the externally observed interference fringes. The internal representation of W is described by a set of Hamilton equations of motion, by which quantum trajectories of a particle moving in W 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.

Quantum‐classical transition of the dissipative wave packet dynamics for barrier scattering

“…Thus, Equations (19) and (23) indicate that the Ehrenfest theorem derived from the transition equation for dissipative systems in Equation (1) holds for all the values of ϵ.…”

“…For example, a detailed analysis has been carried out for a driven triple‐well potential using quantum trajectories . Complex‐valued quantum trajectories have been employed to study quantum systems, including Coulombic systems, the hydrogen molecule ion, the interference fringes in slit experiments, the electric, magnetic, and thermal effects on a quantum dot, and chaotic trajectories in complex space . In addition, the quantum trajectory formulation has been employed to study quantum dissipative systems .…”

Trajectory description of the quantum–classical transition for wave packet interference

“…Based on the complex quantum HamiltonJacobi formalism [36,37], the complex QTM has been used to analyze both stationary bound and scattering state problems [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. Quantum interference demonstrated by the head-on collision of two Gaussian wave packets has been thoroughly analyzed using complex quantum trajectories [53][54][55].…”

Quantum‐classical transition equation with complex trajectories

“…In addition to computational applications, the complex quantum hydrodynamic representation leads to novel trajectory‐based pictures of quantum mechanics. For example, complex quantum trajectories determined from the analytical form of the wave function have been analyzed for several stationary and nonstationary state problems . Quantum interference demonstrated by the head‐on collision of two Gaussian wave packets has been explored in the complex plane .…”