相关论文: Heron Variables in 3-body Coulomb Problem
Taking the Hydrogen atom as an example it is shown that if the symmetry of a three-dimensional system is $O(2) \oplus Z_2$, the variables $(r, \rho, \varphi)$ allow a separation of the variable $\varphi$, and the eigenfunctions define a new…
We discuss the existence of eigenvalues for a third order boundary value problem subject to functional boundary conditions and higher order derivative dependence in the nonlinearities. We prove the existence of positive and negative…
We study an initial-boundary value problem of three-dimensional (3D) compressible isentropic magneto-micropolar fluid equations with Coulomb force and slip boundary conditions in a bounded simply connected domain, whose boundary has a…
We derive closed formulas for mean values of all powers of r in nonrelativistic and relativistic Coulomb problems in terms of the Hahn and Chebyshev polynomials of a discrete variable. A short review on special functions and solution of the…
We show the existence of Borromean bound states in a one-dimensional quantum three-body system composed of two identical bosons and a distinguishable particle. It is assumed that there is no interaction between the two bosons, while the…
We develop a computationally and numerically efficient method to calculate binding energies and corresponding wave functions of quantum mechanical three-body problems in low dimensions. Our approach exploits the tensor structure of the…
Bell non-locality represents the ultimate consequence of quantum entanglement, fundamentally undermining the classical tenet that spatially-separated degrees of freedom possess objective attributes independently of the act of their…
We evaluate different properties of baryons with a heavy c or b quark. The use of Heavy Quark Symmetry (HQS) provides with an important simplification of the non relativistic three body problem which can be solved by means of a simple…
The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent…
An approach is developed to find approximate solutions to the restricted circular three body problem. The solution is useful in approximately describing the position vectors of three spherically symmetric masses, one of which has a much…
The perturbation theory with respect to the potential energy of three particles is considered. The first-order correction to the continuum wave function of three free particles is derived. It is shown that the use of the collective…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
We expose the relation between the properties of the three-body continuum states and their two-body subsystems. These properties refer to their bound and virtual states and resonances, all defined as poles of the $S$-matrix. For one…
The Dirac equation with the Coulomb potential is studied. It is shown that there exists a new invariant in addition to the known Dirac and Johnson-Lippman ones. The solution of the Dirac equation, using the generalized invariant, and…
In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…
We present local existence theorem of the initial value problem for third order semilinear dispersive partial differential equations in two space dimensions. This type of equations arises in the study of gravity wave of deep water, and…
Most physical systems, whether classical or quantum mechanical, exhibit spherical symmetry. Angular momentum, denoted as $\ell$, is a conserved quantity that appears in the centrifugal potential when a particle moves under the influence of…
The Coulomb problem for vector bosons W incorporates a well known difficulty; the charge of the boson localized in a close vicinity of the attractive Coulomb center proves be infinite. This fact contradicts the renormalizability of the…
In this article we study constrained variational problems in one independent variable defined on the space of integral curves of a Frenet system in a homogeneous space G/H. We prove that if the Lagrangian is G-invariant and coisotropic then…
Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian…