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The possibility to recover the which-way information, for example in the two slit experiment, is based on a natural but implicit assumption about the position of a particle {\it before} a position measurement is performed on it. This…
The problem of the availability of trajectories for the Feynman path integral is considered. Forbidden trajectories for single particle integrals are featured in the case of quantum tunneling across barriers. In the case of multiparticle…
Canonical quantum formalism predicts that the interference pattern registered in multi-slit experiments should be a simple combination of patterns observed in two-slit experiments. This has been linked to the validity of Born's rule and…
{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet,…
Using improper Riemann integrals, we will formulate a rigorous version of the real-time, time-sliced Feynman path integral for the $L^2$ transition probability amplitude. We will do this for nonvector potential Hamiltonians with potential…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
It is commonly assumed that no accurate experimental information can be obtained on the path taken by a particle when quantum interference between the paths is observed. However, recent progress in the measurement and control of quantum…
The Feynman path integral has revolutionized modern approaches to quantum physics. Although the path integral formalism has proven very successful and spawned several approximation schemes, the direct evaluation of real-time path integrals…
We present a new experimental approach using a three-path interferometer and find a tighter empirical upper bound on possible violations of Born's Rule. A deviation from Born's rule would result in multi-order interference. Among the…
Quantum walks constitute important tools in different applications, especially in quantum algorithms. To a great extent their usefulness is due to unusual diffusive features, allowing much faster spreading than their classical counterparts.…
The Feynman path integral does not allow a "one real path" interpretation, because amplitudes contribute to probabilities in a non-separable manner. The opposite extreme, "all paths happen", is not a useful or informative account. In this…
Path integrals developed by Richard Feynman have been an important tool in Physics in studying quantum field theory. In mathematics, it has also been widely used in providing formal proofs in the study of Index theorem and asymptotic…
The double slit experiment provides a classic example of both interference and the effect of observation in quantum physics. When particles are sent individually through a pair of slits, a wave-like interference pattern develops, but no…
Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is…
It is notorious that quantum mechanics cannot predict well-defined values for all physical quantities. Less well-known, however, is the fact that quantum mechanics is unable to furnish -- without additional assumptions -- probabilistic…
This model is one of the possible geometrical interpretations of Quantum Mechanics where found to every image Path correspondence the geodesic trajectory of classical test particles in the random geometry of the stochastic fields…
Hardy's paradox is analysed within Feynman's formulation of quantum mechanics. A transition amplitude is represented as a sum over virtual paths which different intermediate measurements convert into different sets of real pathways.…
The Young double-slit interference pattern produced by quantum objects, like photons, that move through a double-slit is regarded, by the conventional Copenhagen interpretation of Quantum Mechanics, as the evidence of the wave-like…
We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry or four-fold symmetry. In this work - the first of a pair…
In this paper, we apply the full new method of quantum theory to study the double-slit diffraction of ${C_{60}}$ molecules. We calculate the double-slit wave functions of ${C_{60}}$ molecules by Schr\"{o}dinger equation, and calculate the…