Related papers: Derivation of the wave equation
Using the elementary axioms of special relativity and quantum mechanics we construct a wave equation which generalizes the Schrodinger equation. We also solve the general second and some higher order differential equations.
Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that semiclassical behavior is obtained at large…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
The Korteweg-de Vries equation is known to yield a valid description of surface waves for waves of small amplitude and large wavelength. The equation features a number of conserved integrals, but there is no consensus among scientists as to…
A gravitational wave must be nonlinear to be able to transport its own source, that is, energy and momentum. A physical gravitational wave, therefore, cannot be represented by a solution to a linear wave equation. Relying on this property,…
There are reasons to doubt that making sense of the wave function (other than as a probability algorithm) will help with the project of making sense of quantum mechanics. The consistency of the quantum-mechanical correlation laws with the…
Starting form the Zakharov/Craig-Sulem formulation of the water-waves equations, we prove that one can define a pressure term and hence obtain a solution of the classical Euler equations. It is proved that these results hold in rough…
Aiming at providing an objective motion picture for the microscopic object described by the wave function, new analysis about motion is presented by use of the point set theory in mathematics, through which we show that a new kind of motion…
The quantum superposition principle is reexamined and reformulated based on the adiabatic theorem of quantum mechanics, nonadiabatic dressed states and experimental evidences. The collapse of the wave function and the quantum measurement…
Formally second-order correct, mathematical descriptions of long-crested water waves propagating mainly in one direction are derived. These equations are analogous to the first-order approximations of KdV- or BBM-type. The advantage of…
We advance a famous principle - causality principle - but under a new view. This principle is a principium automatically leading to most fundamental laws of the nature. It is the inner origin of variation, rules evolutionary processes of…
The interaction between two parts in a compound quantum system may be reconsidered more completely than before and some new understandings and conclusions different from current quantum mechanics are obtained, including the conservation law…
In a planetary or satellite system, idealized as n small bodies in initially coplanar, concentric orbits around a large central body, obeying Newtonian point-particle mechanics, resonant perturbations will cause dynamical evolution of the…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
The paper studies the inferences of wave equations for electromagnetic fields when there are gravitational fields at the same time. In the description with the algebra of octonions, the inferences of wave equations are identical with that…
Historically the starting point of wave mechanics is the Planck and Einstein-de Broglie relations for the energy and momentum of a particle, where the momentum is connected to the group velocity of the wave packet. We translate the…
In the mid-19th century, both the laws of mechanics and thermodynamics were known, and both appeared fundamental. This was changed by Boltzmann and Gibbs, who showed that thermodynamics can be *derived*, by applying mechanics to very large…
A new derivation of the Bernoulli equation for water waves in three-dimensional rotating and translating coordinate systems is given. An alternative view on the Bateman-Luke variational principle is presented. The variational principle…
By definition, a wave is a $C^\infty$ solution $u(x,t)$ of the wave equation on $\mathbb R^n$, and a snapshot of the wave $u$ at time $t$ is the function $u_t$ on $\mathbb R^n$ given by $u_t(x)=u(x,t)$. We show that there are infinitely…
The standing wave solution on an idealized mass spring system can be found using straight forward algebra. The solution is found when this system makes jump rope like rotations around an axis.The standing wave forms a constant shape in a…