Related papers: Volkov wave function: its orthonormality and compl…

In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones

The solution of the Dirac equation in the presence of an arbitrary plane wave, corresponding to the so-called Volkov states, has provided an enormous insight in strong-field QED. In [Phys. Rev. A \textbf{103}, 076011 (2021)] a new "fully…

In the present work, we introduce a new $\mathcal{PT}$-symmetric variant of the Klein-Gordon field theoretic problem. We identify the standing wave solutions of the proposed class of equations and analyze their stability. In particular, we…

Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…

We derive analytically some general features of the power-law sensitivity curve. They include an exact parametric equation, a formula for the peak sensitivity and a proof of convexity in log-log plot. A few conceptual points are also…

The relation between equal-time and light-front wave functions is studied using models for which the four-dimensional solution of the Bethe-Salpeter wave function can be obtained. The popular prescription of defining the longitudinal…

A Borg-Marchenko type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N-wave equation. A procedure to solve inverse problem is used for this purpose. The asymptotic condition on the Weyl…

The notion of a physical collapse of the wave function is embodied in dynamical collapse models. These involve a modification of the unitary evolution of the wave function such as to give a dynamical account of collapse. The resulting…

In this paper we apply the formalism of the analytical signal theory to the Schrodinger wavefunction. Making use exclusively of the wave-particle duality and the principle of relativistic covariance, we actually derive the form of the…

As charged particles surpass the speed of light in an optical medium they produce radiation - analogously to the way jet planes surpass the speed of sound and produce a sonic boom. This radiation emission, known as the Cherenkov effect, is…

In spite of the relevance of the proposal introduced in the recent work A. Abedi, N. T. Maitra and E. K. U. Gross, J. Chem. Phys. 137, 22A530, 2012, there is an important ingredient which is missing. Namely, the proof that the norms of the…

Two results on the completeness of maximal solutions to first and second order ordinary differential equations (or inclusions) over complete Riemannian manifolds, with possibly time-dependent metrics, are obtained. Applications to…

In introductions to the subject for a general audience of mathematicians or logicians, the univalence axiom is typically explained by handwaving. This gives rise to several misconceptions, which cannot be properly addressed in the absence…

Giving a new form of the vortex mode equation by a proper change of parameter, our aim is to analyze the point and contact symmetries of the new equation. Fundamental invariants and a form of general solutions of point transformations along…

Wave-particle duality is one of the fundamental properties of matter and at the same time, one of the mysteries of modern physics. In this paper, we propose and analyze a new interpretation of the wave-particle duality, and propose a new…

We consider some of the methods that can be used to reveal the general features of how wave functions evolve with time in the harmonic oscillator. We first review the periodicity properties over each multiple of a quarter of the classical…

The undoing of quantum measurements is discussed in the broader context of irreversibility in physics. We give explicit examples of how a wavefunction can be uncollapsed in two solid-state experimental set-ups. Wavefunction uncollapse shows…

We study non-scattering phenomena associated with the time-harmonic Helmholtz equation in two dimensions. For very general classes of star-shaped domains, we show that there are at most finitely many wave numbers such that Herglotz incident…

The existence of stationary solitary waves in symmetric and non-symmetric complex potentials is studied by means of Melnikov's perturbation method. The latter provides analytical conditions for the existence of such waves that bifurcate…

Current status of (the lack of) understanding Blazhko effect is reviewed. We focus mostly on the various components of the failure of the models and touch upon the observational issues only at a degree needed for the theoretical background.…