Related papers: Hypergeometric Connotations of Quantum Equations
In our previous publications we have introduced a differential calculus on the algebra $U(gl(m))$ based on a new form of the Leibniz rule which differs from that usually employed in Noncommutative Geometry. This differential calculus…
We summarize some our recent results on encoding exact solutions of field equations in Einstein and modified gravity theories into solitonic hierarchies derived for nonholonomic curve flows with associated bi-Hamilton structure. We argue…
Using well-known methods we generalize (hyper)virial theorems to case of singular potential. Discussion is carried on for most general second order differential equation, which involves all physically interesting cases, such as…
The interplay between quantum theory and general relativity remains one of the main challenges of modern physics. A renewed interest in the low-energy limit is driven by the prospect of new experiments that could probe this interface. Here…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
We present a new step in the foundation of quantum field theory with the tools of scale relativity. Previously, quantum motion equations (Schr\"odinger, Klein-Gordon, Dirac, Pauli) have been derived as geodesic equations written with a…
The massless Klein--Gordon equation on arbitrary curved backgrounds allows for solutions which develop "tails" inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost sixty years…
Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…
We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.
The wave equation is derived for quark pairs in color superconductor in the regime of low density / strong coupling.
We study the three-dimensional Dirac and Klein-Gordon equations with scalar and vector potentials of equal magnitudes as an attempt to give a proper physical interpretation of this class of problems which has recently been accumulating…
Generalizations of the Hamilton-Jacobi and Schrodinger equations for multidimensional variational problems of field theory are deduced. These generalizations are so-called variational differential equations.
We obtain generally covariant operator-valued geodesic equations on a pseudo-Riemannian manifold $M$ as part of the construction of quantum geodesics on the algebra $D(M)$ of differential operators. Geodesic motion arises here as an…
Using well-known methods we generalize (hyper)virial theorems to case of singular potential. Discussion is performed for most general second order differential equation, which involves all physically interesting cases, as Schrodinger and…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…
New exactly solvable quantum models are obtained with the help of the supersymmetric extencion of the nonstationary Schr/"odinger equation.
In this article we introduce a new class of non-Archimedean pseudodifferential equations of Klein-Gordon type and study the corresponding Cauchy problem for these equations. A remarkable fact is that the non-Archimedean Klein-Gordon…
We embed Nelson's stochastic quantization in the Schwartz-Meyer second order geometry framework. The result is a non-perturbative theory of quantum mechanics on (pseudo)-Riemannian manifolds. Within this approach, we derive stochastic…
Quantum geometrodynamics (QGD) in extended phase space essentially distinguished from the Wheeler - DeWitt QGD is proposed. The grounds for constructing a new version of quantum geometrodynamics are briefly discussed. The main part in the…
The Schr\" odinger equations which are exactly solvable in terms of associated special functions are directly related to some self-adjoint operators defined in the theory of hypergeometric type equations. The fundamental formulae occurring…