Related papers: Facets of the spinless Salpeter equation
Starting from the formal expressions of the hydrodynamical (or ``local'') quantities employed in the applications of Clifford Algebras to quantum mechanics, we introduce --in terms of the ordinary tensorial framework-- a new definition for…
Lorentz transformation equations provide us a set of relations between the spacetime coordinates as observed from two different inertial frames. In case, one of the frames is moving with a uniform rectilinear acceleration we have Rindler's…
The procedure of the "quantum" linearization of the Hamiltonian ordinary differential equations with one degree of freedom is introduced. It is offered to be used for the classification of integrable equations of the Painleve type. By this…
Approximate bound state solutions of the spinless Salpeter equation for the Hellmann potential are studied for heavy particles. By using functional analysis method, an analytical expression for the energy levels, and the corresponding…
Besides perturbation theory, which requires, of course, the knowledge of the exact unperturbed solution, variational techniques represent the main tool for any investigation of the eigenvalue problem of some semibounded operator H in…
We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear…
In this paper we consider the simplest functional Schroedinger equation of a quantum field theory (in particular QCD) and study its solutions. We observe that the solutions to this equation must possess a number of properties. Its Taylor…
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies…
On the basis of an algebraic relation between torsion and a classical spinor field a new interpretation of Einstein-Cartan gravity interacting with classical spinor field is proposed. In this approach the spinor field becomes an auxiliary…
We address the universal applicability of the discrete nonlinear Schroedinger equation. By employing an original but general top-down/bottom-up procedure based on symmetry analysis to the case of optical lattices, we derive the most widely…
Irrotational ow of a spherical thin liquid layer surrounding a rigid core is described using the defocusing nonlinear Schrodinger equation. Accordingly, azimuthal moving nonlinear waves are modeled by periodic dark solitons expressed by…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
The inherently homogeneous stationary-state and time-dependent Schroedinger equations are often recast into inhomogeneous form in order to resolve their solution nonuniqueness. The inhomogeneous term can impose an initial condition or, for…
A general form for the equation of motion for higher-curvature gravity is obtained. The interesting feature of the analysis is that it can handle Lagrangians which contain non-minimal kinetic scalar couplings. Certain subtle features, which…
We study a general class of PT-symmetric tridiagonal Hamiltonians with purely imaginary interaction terms in the quasi-hermitian representation of quantum mechanics. Our general Hamiltonian encompasses many previously studied lattice models…
We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial…
It is shown that non-stationary solutions of the Schr\"{o}dinger equation, which describes the quantum dynamics of a particle in the field of a one-dimensional delta potential (1DDP), are divided into two classes: some define pure states…