Related papers: Quaternionic potentials in non-relativistic quantu…
This article is the second in a series of two presenting the Scale Relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. Here, we show Schroedinger's equation to be a reformulation of Newton's…
A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its…
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…
We discuss basic potentials of the nonrelativistic and relativistic quantum mechanics that can be integrated in the Nikiforov and Uvarov paradigm with the aid of a computer algebra system. This consideration may help the readers to study…
It is proposed that the Schrodinger equation for a free point particle has non-linear corrections which depend on the mass of the particle. It is assumed that the corrections become extremely small when the mass is much smaller or much…
Plasmas are usually described using classical equations. While this is often a good approximation, where are situations when a quantum description is motivated. In this paper we will include several quantum effects, ranging from particle…
After a review on recent results on quaternic quantum mechanics ($\mathbb{H}$QM), we present further consistency tests that reinforce its compatibility with the usual complex quantum mechanics ($\mathbb{C}$QM). The novel results comprises…
We handle all the self-adjoint extensions of the minimal Schroedinger operator for the non-relativistic electron living in the one-dimensional configuration space with a junction. We are interested in every boundary condition corresponding…
A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we…
Many wave phenomena are related to interactions. Considering once neglected interactions in some cases, states of large objects and Newton's idea about measurement, we attempt to modify some concepts and principles of non-relativistic…
The azimuthal hadronic flow observed in ultra-relativistic ion-ion collisions provides a sensitive probe of many-body ground-state correlations in the colliding nuclei. In particular, collective correlations associated with nuclear…
We consider interactions of scalar particles, photons, and fermions in Schwarzschild, Reissner-Nordstr\"om, Kerr, and Kerr-Newman gravitational and electromagnetic fields with a zero and nonzero cosmological constant. We also consider…
A new formulation of potential scattering in quantum mechanics is developed using a close structural analogy between partial waves and the classical dynamics of many non-interacting fields. Using a canonical formalism we find non-linear…
While it is widely believed that gravity should ultimately be treated as a quantum theory, there remains a possibility that general relativity should not be quantized. If this is the case, the coupling of classical gravity to the…
We report on a theoreticl study of the electronic structure of quasiperiodic, quasi-one-dimensional systems where fully three dimensional interaction potentials are taken into account. In our approach, the actual physical potential acting…
The quantum mechanical motion of a relativistic particle in a non-continuous spacetime is investigated. The spacetime model is a dense, rationale subset of two-dimensional Minkowski spacetime. Solutions of the Dirac equation are calculated…
The dynamics of relativistic (scalar and vector) bosons through nonminimal vector square (well and barrier) potentials is studied in the Duffin-Kemmer-Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrodinger…
In this study, the Schrodinger equation for flat potentials through the pseudo-perspective method is investigated.
An exactly solvable position-dependent mass Schr\"odinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems…
Quantum Brownian motion in a periodic cosine potential is studied and a simple estimate of the tunneling effect is obtained in the frames of a quasi-equilibrium semiclassical approach. It is shown that the latter is applicable for heavy…