Related papers: Wigner's effective mathematics and contradiction
Wigner's quantum-mechanical classification of particle-types in terms of irreducible representations of the Poincar\'e group has a classical analogue, which we extend in this paper. We study the compactness properties of the resulting phase…
Additivity of Breit-Wigner phases has been proposed to describe interfering resonances in partial waves in $\pi\pi$ scattering. This assumption leads to an expression for partial wave amplitudes that involves products of Breit-Wigner…
An exactly solvable time-dependent quantum mechanical problem is employed to study the convergence properties of transition amplitudes calculated by using the Schwinger variational principle. A detailed comparison between the amplitudes…
A scalar Wigner distribution function for describing polarized light is proposed in analogy with the treatment of spin variables in quantum kinetic theory. The formalism is applied to the propagation of circularly polarized light in…
We prove a formula expressing the gradient of the phase function of a function $f: \mathbb R^d \mapsto \mathbb C$ as a normalized first frequency moment of the Wigner distribution for fixed time. The formula holds when $f$ is the Fourier…
Sharp Strichartz estimates are proved for Schr\"odinger and wave equations with Lipschitz coefficients satisfying additional structural assumptions. We use Phillips functional calculus as a substitute for Fourier inversion, which shows how…
The diffraction of a time-harmonic plane wave on collinear finite defects in a square lattice is studied. This problem is reduced to a matrix Wiener-Hopf equation. This work adapts the recently developed iterative Wiener-Hopf method to this…
The problem of Schr\"odinger propagation of a discontinuous wavefunction -diffraction in time- is studied under a new light. It is shown that the evolution map in phase space induces a set of affine transformations on discontinuous…
Traditionally, the diffraction of a scalar wave satisfying Helmholtz equation through an aperture on an otherwise black screen can be solved approximately by Kirchhoff's integral over the aperture. Rubinowicz, on the other hand, was able to…
The Gutzwiller trace formula is extended to include diffraction effects. The new trace formula involves periodic rays which have non-geometrical segments as a result of diffraction on the surfaces and edges of the scatter.
Much of the discussion of decoherence has been in terms of a particle moving in one dimension that is placed in an initial superposition state (a Schr\"{o}dinger "cat" state) corresponding to two widely separated wave packets. Decoherence…
We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential…
There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current~$\bf J$. This current reveals fine details of quantum dynamics -- finer than is…
We have analytically explored the Rayleigh-Sommerfeld scalar diffraction for oblique incidence. We have explicitly derived the Fraunhofer diffraction formulae for oblique incidence of plane scalar wave on various apertures, such as…
We have considered optical beams with phase singularity and experimentally verified that these beams, although being classical, have properties of two mode entanglement in quantum states. We have observed the violation of Bell's inequality…
We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a…
Representations of the Poincar\'{e} symmetry are studied by using a Hilbert space with a phase space content. The states are described by wave functions ( quasi amplitudes of probability) associated with Wigner functions (quasi probability…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
It is shown how a physical function, namely the Wigner function, that in principle may be measured, can be used to evaluate divergent series.
The representation of quantum states via phase-space functions constitutes an intuitive technique to characterize light. However, the reconstruction of such distributions is challenging as it demands specific types of detectors and detailed…