Related papers: The new wave equations of relativistic and non-rel…
It is well known that Schr\"{o}dinger's equation is only suitable for the particle in conservative force field. In atomic and molecular field, a particle can suffer the action of non-conservative force. In this paper, a new quantum wave…
The variational method in a reformulated Hamiltonian formalism of Quantum Electrodynamics is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels…
In this work, we follow the idea of the De Broglie's matter waves and the analogous method that Schr\"{o}dinger founded wave equation, but we apply the more essential Hamilton principle instead of the minimum action principle of Jacobi…
Relativistic quantum mechanics can be considered to have begun with a search for wave equations corresponding to each intrinsic spin. However, relativistic quantum physics differs fundamentally from the non-relativistic wave mechanics. It…
A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
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…
Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role,…
A nonrelativistic equation for the system of two interacting particles within the framework of a model with noncommuting operators of coordinates and momenta of different particles is proposed, and a self-consistent system of equations for…
We demonstrate how one can describe explicitly the present arbitrariness in solutions of relativistic wave equations in external electromagnetic fields of special form. This arbitrariness is connected to the existence of a transformation,…
There are important differences between the nonrelativistic and relativistic description of electron beams. The orbital angular momentum quantum number cannot be used to specify the wave functions in the relativistic case. In this Letter we…
The irreducible representations of the extended Galilean group are used to derive infinite sets of symmetric and asymmetric second-order differential equations with constant coeffcients. All derived equations are local and their Lagrangians…
Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence.
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…
In contrast to wave functions in nonrelativistic quantum mechanics interpreted as probability amplitudes, wave functions in relativistic quantum mechanics have generalized meanings such as charge-density amplitudes, energy-density…
Newton's second law may be used to obtain a wave equation, which reduces to Schrodinger's equation in the nonrelativistic limit and for a conservative force.
The relativistic quantum mechanics equations for the electromagnetic interaction are propososed.
The quantum hydrodynamic-like equations for two real variables (i.e., the phase and the amplitude of the wave function) of the relativistic Klein-Gordon equation are derived in the present paper. The paper also shows that in classical limit…
It is shown that the Schr\"{o}dinger nonrelativistic equation of a system of interacting particles is not a rigorously nonrelativistic equation since it is based on the implicit assumption of finiteness of the interaction propagation…
In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein-Gordon wavefunctions, as special cases; and then in turn for non-relativistic…