Related papers: The Snell law for quaternionic potentials
Using the quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, we construct a Lagrangian of a quantum system in one dimension and derive a third order equation of motion representing a first integral of the…
We theoretically investigate the optical force exerted on an isotropic particle illuminated by a superposition of plane waves. We derive explicit analytical expressions for the exerted force up to quadrupolar polarizabilities. Based on…
Disclosure of scaling relationship between observable quantities gives direct information about dynamics of natural phenomenon. This is the main reason why scaling plays a key role in the methodology of natural sciences. In this talk, Part…
Self-similar solutions to the problem of a special relativistic law of motion for thin shells of matter are calculated. These solutions represent the special relativistic generalization of momentum conservation for the thin layer…
The behavior of classical and quantum wave beams in stationary media is shown to be ruled by a "Wave Potential" function encoded in Helmholtz-like equations, determined by the structure itself of the beam and taking, in the quantum case,…
Crossing symmetry asserts that particles are indistinguishable from anti-particles traveling back in time. In quantum field theory, this statement translates to the long-standing conjecture that probabilities for observing the two scenarios…
The optical potential is a powerful instrument for calculations on a wide variety of nuclear reactions, in particular, for quasi-elastic lepton-nucleus scattering. Phenomenological optical potentials are successful in the description of…
From the relativistic law of motion we attempt to deduce the field theories corresponding to the force law being linear and quadratic in 4-velocity of the particle. The linear law leads to the vector gauge theory which could be the abelian…
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions.…
An interesting idea, dating back to Feynman, argues that quantum mechanics may break down for large masses if one entertains the possibility that gravity can be "classical", thereby leading to predictions different from conventional…
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian…
We consider integrable spherical analogue of the Darboux potential, which appear in the problem (and its generalizations) of the planar motion of a particle in the field of two and four fixed Newtonian centers. The obtained results can be…
Scattering discussion due to Double Dirac Equation in Quaternionic version of relativistic quantum mechanics has been studied in this paper in details. In such a quantum mechanics Dirac equation in presence vector and scalar potential has…
Using Feynman's representation of the quantum evolution and considering a quantum particle as a matter field (continuous medium), it is shown that individual particles of the field have unique paths of the motion. This allows describing…
Quantum mechanics states that a particle emitted at point (x_1,t_1) and detected at point (x_2,t_2) does not travel along a definite path between the two points. This conclusion arises essentially from the analysis of the two-slit…
It has been found that quantum corrections can substantially affect the classical results of tracking for trajectories close to the separatrix. Hence the development of a basic formalism for obtaining the quantum maps for any particle beam…
It is shown that the supersymmetric quantum mechanics has an octonionic generalization. The generalization is based on the inclusion of quaternions into octonions. The elements from the coset octonions/quaternions are unobservables bacause…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
We discuss applications of the quantile concept of trajectories and velocities to the propagation of electromagnetic signals in wave guides of varying cross section. Quantile motion is a general description of the transport properties of…
Experimental studies of infinite (unrestricted at least in one direction) quantum particle motion using probe nanotechnologies have revealed the necessity of revising previous concepts of their motion. Particularly, quantum particles…