Related papers: Relativistic Wave Equations: An Operational Approa…
An exact, ray-based general treatment is shown to hold for any kind of monochromatic wave feature - including diffraction and interference - described by Helmholtz-like equations, under the coupling action of a dispersive function (which we…
We define a class of pseudo-differential operators in a completely new way, which is called the abstract operators and expounded systematically the theory of abstract operators. By combining abstract operators with the Laplace transform, we…
The formulation of a rigid body in relativistic quantum mechanics is studied. Departing from an alternate approach at the relativistic classical level, the corresponding Klein-Gordon and Dirac operators for the rigid body are obtained in…
The auxiliary functions provide efficient computation of integrals arising at the self-consistent field (SCF) level for molecules using Slater-type bases. This applies both in relativistic and non-relativistic electronic structure theory.…
Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation…
Based on the Dirac approach we have developed the relativistic vision of the WKB method for centrally symmetrical potential with mixed Lorenz structure. We have obtained relativistic wavefunctions of light quark and the new rule of…
Schrodinger equation with two-component wave function which describes a relativistic spin 1/2 particle in a weak electromagnetic field is obtained. In the same approximation Schrodinger equation with traditional norm condition and…
In this note we give an explicit formula for the wave equation associated to the Schrodinger operator with a Liouville Potential with applications to the telegraph equation as well as the wave equation on the hyperbolic plane
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
We study classical solutions (existence, uniqueness, and explicit solution operator) for homogeneous, linear, and semilinear abstract Volterra integral equations of wave type with almost sectorial operators. We use a functional calculus for…
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
We present new exact solutions (in 3+1 and 2+1 dimensions) of relativistic wave equations (Klein-Gordon and Dirac) in external electromagnetic fields of special form. These fields are combinations of Aharonov-Bohm solenoid field and some…
In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a `relaxed' variational principle, i.e., on a Lagrangian involving as many…
Relativistic potential-type equations are proposed which approximately reproduce important features and constraints of field-theoretic models and can be useful tool in hadron spectroscopy. Within this approach, the Regge-trajectory…
A new Hamiltonian formulation for the fully nonlinear water-wave problem over variable bathymetry is derived, using an exact, vertical series expansion of the velocity potential, in conjunction with Luke's variational principle. The…
The classical relativistic wave equations are presented as partial difference equations in the arena of covariant discrete phase space. These equations are also expressed as difference-differential equations in discrete phase space and…
We prove existence of modified wave operators for one-dimensional Schr\"odinger equations with potential in $L^p(\reals)$, $p<2$. If in addition the potential is conditionally integrable, then the usual M\"oller wave operators exist. We…
Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave…
The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with…
A generalization of the stochastic wave function method is presented which allows the unravelling of arbitrary linear quantum master equations which are not necessarily in Lindblad form and, moreover, the explicit treatment of memory…