相关论文: Photon position eigenvectors lead to complete phot…

In this paper we undertake an analysis of the eigenstates of two non self-adjoint operators $\hat q$ and $\hat p$ similar, in a suitable sense, to the self-adjoint position and momentum operators $\hat q_0$ and $\hat p_0$ usually adopted in…

This paper is a continuation of our previous works about coordinate, momentum, dispersion operators and phase space representation of quantum mechanics. It concerns a study on the properties of wavefunctions in the phase space…

Photon wave function is a controversial concept. Controversies stem from the fact that photon wave functions can not have all the properties of the Schroedinger wave functions of nonrelativistic wave mechanics. Insistence on those…

Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…

In a recent article [Foo et. al., Nature Comms. 13, 2 (2022)], we devised a method of constructing the Lorentz-covariant Bohmian trajectories of single photons via weak measurements of the photon's momentum and energy. However, whether such…

We treat the quantum dynamics of a harmonic oscillator as well as its inverted counterpart in the Schr\"odinger picture. Generally in the most papers of the literature, the inverted harmonic oscillator is formally obtained from the harmonic…

The polarization operator in a constant and homogeneous magnetic field of arbitrary strength is investigated on mass shell. The calculations are carried out at all photon energies higher the pair creation threshold as well as lower this…

The light-cone Photon wave function in explicit helicity states, valid for massive quarks and in both momentum and configuration space, is presented by considering the leading order photon-proton hard scattering, i.e., the splitting quark…

We develop relativistic non-Hermitian quantum theory and its application to neutrino physics in a strong magnetic field. It is well known, that one of the fundamental postulates of quantum theory is the requirement of Hermiticity of…

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the…

Over the last two decades, advances in fabrication have led to significant progress in creating patterned heterostructures that support either carriers, such as electrons or holes, with specific band structure or electromagnetic waves with…

In this paper the relativistic quantum mechanics is considered in the framework of the nonstandard synchronization scheme for clocks. Such a synchronization preserves Poincar{\'e} covariance but (at least formally) distinguishes an inertial…

It is shown that the quantum jumps in the photon number n from zero to one or more photons induced by backaction evasion quantum nondemolition measurements of a quadrature component x of the vacuum light field state are strongly correlated…

We develop the quantum theory of transverse angular momentum of light beams. The theory applies to paraxial and quasi-paraxial photon beams in vacuum, and reproduces the known results for classical beams when applied to coherent states of…

In quantum mechanics, spatial wavefunctions describe distributions of a particle's position or momentum, but not of angular momentum $j$. In contrast, here we show that a spatial wavefunction, $j_m (\phi,\theta,\chi)=~e^{i m \phi} \delta…

An experiment is presented in which the alleged progression of a photon's wave function is ``measured'' by a row of superposed atoms. The photon's wave function affects only one out of the atoms, regardless of its position within the row,…

Photons propagating in strong magnetic fields are subject to a phenomenon called the "vacuum birefringence" where refractive indices of two physical modes both deviate from unity and are different from each other. We compute the vacuum…

In the recent years a generalization $H=p^2 +x^2(ix)^\epsilon$ of the harmonic oscillator using a complex deformation was investigated, where \epsilon\ is a real parameter. Here, we will consider the most simple case: \epsilon even and x…

A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…

The aim of this paper is to bring into the picture a new phenomenon in the theory of orthogonal matrix polynomials satisfying second order differential equations. The last few years have witnessed some examples of a (fixed) family of…