Related papers: Feinberg-Horodecki Equation with P\"oschl-Teller P…
Analytical solutions to the time-dependent Shr\"{o}dinger equation in one dimension are developed for time-independent potentials, one consisting of an infinite wall and a repulsive delta function. An exact solution is obtained by means of…
We are developing a covariant model for all mesons that can be described as quark-antiquark bound states in the framework of the Covariant Spectator Theory (CST) in Minkowski space. The kernel of the bound-state equation contains a…
We use special quadrature formulas for singular and hypersingular integral to numerically solve the Schr\"{o}dinger equation in momentum space with the linear confinement potential, Coulomb and Cornell potentials. It is shown that the…
We examine in greater detail the proposal that time is the conjugate of the constants of nature. Fundamentally distinct times are associated with different constants, a situation often found in "relational time" settings. We show in detail…
In the paper we derive two formulas representing solutions of Cauchy problem for two Schr\"{o}dinger equations: one-dimensional momentum space equation with polynomial potential, and multidimensional position space equation with locally…
We prove a local in time well-posedness result for quasi-linear Hamiltonian Schr\"odinger equations on $\mathbb{T}^d$ for any $d\geq 1$. For any initial condition in the Sobolev space $H^s$, with $s$ large, we prove the existence and…
In this paper, we study spatially homogeneous solutions of the Boltzmann equation in special relativity and in Robertson-Walker spacetimes. We obtain an analogue of the Povzner inequality in the relativistic case and use it to prove global…
This is an abstract of authors PhD thesis which is devoted to studies of quantum field models with strong coupling. The {\em Schwinger-Dyson equations} (SDEs) in momentum representation are solved in Minkowski space. The original version of…
One construction of exactly-solvable potentials for Fokker-Planck equation is considered based on supersymmetric quantum mechanics approach.
By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schr\"odinger equation (INLSE). This is…
A supersymmetric technique for the solution of the effective mass Schr\"{o}% dinger equation is proposed. Exact solutions of the Schroedinger equation corresponding to a number of potentials are obtained. The potentials are fully…
We investigate the existence of inhomogeneous Szekeres spacetimes in Einstein-\ae ther theory. We show that inhomogeneous solutions which can be seen as extension of the Szekeres solutions existing in Einstein-\ae ther gravity only for a…
In this paper, the space-fractional Schr\"{o}dinger equations with singular potentials are studied. Delta-like or even higher-order singularities are allowed. By using the regularising techniques, we introduce a family of 'weakened'…
We propose a time-varying parameter $\underline{\alpha}$ for G\"{o}del metric and an energy momentum tensor corresponding to this geometry is found. To satisfy covariance arguments time-varying gravitational and cosmological term are…
We attack the specific time-dependent Hamiltonian problem H=-{1/2} (t_o/t)^a \partial_{xx} + (1/2) \omega^2 (t/t_o)^b x^2. This corresponds to a time-dependent mass (TM) Schr\"odinger equation. We give the specific transformations to a…
In this paper we have generalized the quantum mechanics on fractal time-space. The time is changing on Cantor-set like but space is considered as fractal curve like Von-Koch curve. The Feynman path method in quantum mechanics has been…
The Schr\"odinger-Coulomb Sturmian problem in $\mathbb{R}^{N}$, $N\geqslant2$, is considered in the momentum representation. An integral formula for the Gegenbauer polynomials, found recently by Cohl [arXiv:1105.2735], is used to separate…
In this work, we obtain all spatially homogeneous space-time models related to the intersection of the set of St\"ackel spaces of type (2.1) and the set of conformally St\"ackel spaces of type (3.1). These models allow a complete separation…
We construct coherent states using sequences of combinatorial numbers such as various binomial and trinomial numbers, and Bell and Catalan numbers. We show that these states satisfy the condition of the resolution of unity in a natural way.…
Space-time--time is a natural hybrid of Kaluza's five-dimensional geometry and Weyl's conformal space-time geometry. Translations along the secondary time dimension produce the electromagnetic gauge transformations of Kaluza--Klein theory…