Related papers: Schroedinger discovery of wave mechanics
Using a variational formulation, we show that Schrodinger's 4th-order, real-valued matter-wave equation which involves the spatial derivatives of the potential V(r), produces the precise eigenvalues of Schrodinger's 2nd-order,…
The discovery of Berry and Balazs in 1979 that the free-particle Schr\"odinger equation allows a non-dispersive and accelerating Airy-packet solution has taken the folklore of quantum mechanics by surprise. Over the years, this intriguing…
The past four years have seen a scientific revolution through the birth of a new field: gravitational-wave astronomy. The first detection of gravitational waves---recognised by the 2017 Nobel Prize in Physics---provided unprecedented tests…
On December 14. 1900, Max Planck communicated his derivation of his radiation formula, which he later called ``an act of desperation''. This date is widely recognized as birthday of quantum theory. For Planck it meant the end of his…
Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are…
Steven Weinberg productive scientific life teaches us many things, one of the most important of which is the power of his example. This essay contains personal reminiscences and a speculation about gravitational wave propagation based on…
Hubble's announcement of the magnitude-redshift relation \cite{Hub29} brought about a major change in our understanding of the Universe. After tracing the pre-history of Hubble's work, and the hiatus in our understanding which his…
We set up the classical wave equation for a particle formed of an oscillatory zero-rest-mass charge together with its resulting electromagnetic waves, traveling in a potential field $V$ in a susceptible vacuum. The waves are…
A new approach to find exact solutions to one--dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known…
The LIGO results are among the greatest experimental achievements of all times. Time and again scientists have compared this feat to Galileo pointing his telescope to the sky, offering instead an 'ear' to the cosmos. After the remarkable…
This colloquium summarizes Dirac's contributions to the discovery of quantum mechanics before he invented his relativistic wave equation.
The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schr\"odinger equation (NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking the…
In 1981 Edward Witten proved a remarkable result where he derived the classical Morse Inequalities using ideas from Supersymmetric (SUSY) Quantum Mechanics. In this regard, one has an example where a Physical Theory has something to say…
All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schrodinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a…
Quasi-periodic Schr\"odinger-type operators naturally arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the…
It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic…
For steady-state and some other types of mechanical waves of an arbitrary form, intensity and nature, propagating in a free uniform waveguide, we present the following. Relations for the axial momentum as it directly follows from the…
This contribution is divided in two parts. The first part provides a text-book level introduction to gravitational radiation. The key concepts required for a discussion of gravitational-wave physics are introduced. In particular, the…
Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Schr\"odinger equation is often used to model rogue waves; it…
The observation of primordial gravitational waves could provide a new and unique window on the earliest moments in the history of the universe, and on possible new physics at energies many orders of magnitude beyond those accessible at…