Related papers: The ground state energy of a charged particle on a…
We consider the translationally invariant Pauli-Fierz model describing a charged particle interacting with the electromagnetic field. We show under natural assumptions that the fiber Hamiltonian at zero momentum has a ground state.
Finding the ground state energy of the Heisenberg Hamiltonian is an important problem in the field of condensed matter physics. In some configurations, such as the antiferromagnetic translationally-invariant case on the 2D square lattice,…
Energy levels are investigated for two charged particles possessing an attractive, momentum-independent, zero-range interaction in a uniform magnetic field. A transcendental equation governs the spectrum, which is characterized by a…
An electron moving on plane in a uniform magnetic field orthogonal to plane is known as the Landau problem. Wigner functions for the Landau problem when the plane is noncommutative are found employing solutions of the Schroedinger equation…
The energy spectrum of a nonrelativistic particle on a noncommutative sphere in the presence of a magnetic monopole field is calculated. The system is treated in the field theory language, in which the one-particle sector of a charged…
We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking different interaction parameter,…
The dynamics of a spin--1/2 neutral particle possessing electric and magnetic dipole moments interacting with external electric and magnetic fields in noncommutative coordinates is obtained. Noncommutativity of space is interposed in terms…
We consider the so-called semiclassical variant of general relativity, where gravitational field is not quantized but matter is quantized, for the simplest composite quantum body - a hydrogen atom. We create a stationary electron quantum…
We consider the forces acting on electrons in magnetic field including the constraints and a condition arising from quantum mechanics. The force is calculated as the electron mass, $m_e$, multiplied by the total time-derivative of the…
There are several ways to derive Einstein's celebrated formula for the energy of a massive particle at rest, $E=mc^2$. Noether's theorem applied to the relativistic Lagrange function provides an unambiguous and straightforward access to…
We derive the Schroedinger equation for a spinless charged particle constrained to a curved surface with electric and magnetics fields applied. The particle is confined on the surface using a thin-layer procedure, giving rise to the…
The energy characteristics of a relativistic charged particle in the field of a plane electromagnetic wave of a given amplitude are studied. The dependence of the particle's energy on its phase coordinate is obtained. The maximum value of…
We present lattice results for the ground state energy of a spin-1/2 fermion system in the unitary limit, where the effective range of the interaction is zero and the scattering length is infinite. We compute the ground state energy for a…
The purpose of this study is to calculate the entanglement measure for a bipartite system where the two subsystems interact via a central potential, and more importantly, to analyze the conceptual implication in the case of gravitational…
We consider a motion of a weakly relativistic charged particle with an arbitrary spin in central potential $e/r$ in terms of classical mechanics. We show that the spin-orbital interaction causes the precession of the plane of orbit around…
The ground state energy of the Mueller functional of large (neutral) atoms of atomic number Z agrees with the quantum mechanical ground state energy up to order o(Z to the 5/3). ----- Die Grundzustandsenergie des Muellerfunktionals von…
We consider the Fr\"ohlich $N$-polaron Hamiltonian in the strong coupling limit and bound the ground state energy from below. In particular, our lower bound confirms that the ground state energy of the Fr\"ohlich polaron and the ground…
We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$ H=((D-A)\cdot\boldsymbol{\sigma})^2-V $$ with $$V=\sum_{1\le m\le M} \frac{Z_m}{|x-y_m|}$$ and a…
For the $S$ states of two-electron atoms, we introduce an exact and unique factorization of the internal eigenfunction in terms of a marginal amplitude, which depends functionally on the electron-nucleus distances $r_1$ and $r_2$, and a…
The perturbation theory in QED used the new form of ground state as a state of interacted particles is proposed. The mean electromagnetic field of charged elementary particle is calculated. The possibility of elimination the problem with…