Related papers: Derivation of the wave equation
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
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…
The concept of walking wave is introduced from classical relativistic positions. One- and three-dimensional walking waves considered with their wave equations and dispersion equations. It is shown that wave characteristics (de Broglie's and…
In classical mechanics, the motion of an object is described with Newton's three laws of motion, which means that the motion of the material elements composing a continuum can be described with the particle model. However, this viewpoint is…
We state several ideas based on the view-point of particle behaviour of matter to explain wave character of photon and elementary particles. By using Newton's suggestion of light ray, we clarify integrally the behaviour of light ``wave''.…
We calculate certain estimates for the solution of the characteristic problem of the wave equation reduced to first order, in terms of the free data prescribed on two transverse surfaces, one of which is characteristic. Estimates of such…
In this paper we will argue that the superposition of waves can be calculated and taught in a simple way. We show, using the Gauss's method to sum an arithmetic sequence, how we can construct the superposition of waves - with different…
Wave functions are generally written with arguments consisting of sets of ``particle'' coordinates and quantum numbers. Pauli derived a principle governing the exchange of pairs of sets that differ only in their spatial and spin component…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
We research the natural causality of the Universe. We find that the equation of causality provides very good results on physics. That is our first endeavour and success in describing a quantitative expression of the law of causality. Hence,…
The wave kinetic equation has become an important tool in different fields of physics. In particular, for surface gravity waves, it is the backbone of wave forecasting models. Its derivation is based on the Hamiltonian dynamics of surface…
In many introductory-level physics textbooks, the derivation of the formula for the speed of transverse waves in a string is either omitted altogether or presented under physically overly idealized assumptions about the shape of the…
Wave propagation in curved tubular domains is considered. A general version of Webster's equation is derived from the scattering passive wave equation. More precisely, it is shown that planar averages of a sufficiently smooth solution of…
We illustrate a simple derivation of the Schrodinger equation, which requires only knowledge of the electromagnetic wave equation and the basics of Einstein's special theory of relativity. We do this by extending the wave equation for…
Non-relativistic de Broglie-Bohm theory describes particles moving under the guidance of the wave function. In de Broglie's original formulation, the particle dynamics is given by a first-order differential equation. In Bohm's…
Schrodinger path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrodinger equation for the particle wave function, assuming that it has a meaning of…
We argue that quantum mechanics makes sense without such controversial postulates as the wave function collapse, the quantum probability rule and the observable postulate. We only need the existence of a wave function as a representation of…
In this paper, we consider the stabilization of wave equations with moving boundary. First, we show the solution behaviour of wave equation with Neumann boundary conditions, that is, the energy of wave equation with mixed boundary…
Following the spirit of de Broglie and Einstein, we think the concepts of matter and radiation can be unified. We know a particle propagates like a wave; its motion is described by certain wave equations. At this point, it is not clear what…