相关论文: First and second-order relativistic corrections to…
We compute second-order quantum corrections, as quantum dispersions and correlations, to a cosmological model coupling a single scalar perturbation mode to a bouncing background within Loop Quantum Cosmology (LQC). Using an effective…
This paper presents analytical solutions for eigenvalues and eigenfunctions of the Schr\"odinger equation in higher dimensions, incorporating the Dunkl operator. Two fundamental quantum mechanical problems are examined in their exact forms:…
The second order $N$-dimensional Schr\"odinger equation with pseudoharmonic potential is reduced to a first order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution…
Exactly solvable $N$-dimensional model of the quantum isotropic singular oscillator in the relativistic configurational $\vec r_N$-space is proposed. It is shown that through the simple substitutions the finite-difference equation for the…
We present a novel form of relativistic quantum mechanics and demonstrate how to solve it using a recently derived unitary perturbation theory, within partial wave analysis. The theory is tested on a relativistic problem, with two spinless,…
The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. We know that the harmonic oscillator is integrable in…
Doubly Special Relativity (DSR) augments special relativity by introducing, alongside the invariant speed of light $c$, a second observer-independent scale typically associated with the Planck regime. At the level of effective wave…
The idea of adaptive perturbation theory is to divide a Hamiltonian into a solvable part and a perturbation part. The solvable part contains the non-interacting sector and the diagonal elements of Fock space from the interacting terms. The…
We consider the effect of rescattering of pairs of quasiparticles in the Cooper channel resulting in the strong renormalization of second-order corrections to the spin susceptibility in a two-dimensional electron system. We use the Fourier…
This work is a collection of initial calculations and formal considerations within the Salpeter-Sucher exact equal-time relativistic quantum electrodynamics framework. The calculations are carried out as preparation for the computation of…
Oscillatory integral techniques are used to study the well-posedness of the KP-I equation for initial data that are small with respect to the norm of a weighted Sobolev space involving derivatives of total order no larger than 2.
The quantum modes of a new family of relativistic oscillators are studied by using the supersymmetry and shape invariance in a version suitable for (1+1) dimensional relativistic systems. In this way one obtains the Rodrigues formulas of…
We investigate the connection between the linear harmonic oscillator equation and some classes of second order nonlinear ordinary differential equations of Li\'enard and generalized Li\'enard type, which physically describe important…
We derive recursively the perturbation series for the ground-state energy of the D-dimensional anharmonic oscillator and resum it using variational perturbation theory (VPT). From the exponentially fast converging approximants, we extract…
In this paper, we study high order correctors in stochastic homogenization. We consider elliptic equations in divergence form on $\mathbb{Z}^d$, with the random coefficients constructed from i.i.d. random variables. We prove moment bounds…
We compare two opposite ways of performing a 3D reduction of the two-fermion Bethe-Salpeter equation beyond the instantaneous approximation and Salpeter's equation. The more usual method consists in performing an expansion around an…
We use the semi-classical approximation in perturbative scalar quantum electrodynamics to calculate the quantum correction to the Larmor radiation formula to first order in Planck's constant in the non-relativistic approximation, choosing…
The second order perturbative field equations for slowly and rigidly rotating perfect fluid balls of Petrov type D are solved numerically. It is found that all the slowly and rigidly rotating perfect fluid balls up to second order,…
For a class of oscillatory resonant problems, involving Dirichlet problems for semilinear PDE's on balls and rectangles in $R^n$, we show the existence of infinitely many solutions, and study the global solution set. The first harmonic of…
This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin and U. D.…