Related papers: Explicitly symmetrical treatment of three-body pha…

We derive expressions for three-body phase space that are explicitly symmetrical in the masses of the three particles, by three separate methods.

We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…

The energy spectrum of the three-particle Hamiltonian obtained by replacing the two-body trigonometric potential of the Sutherland problem by a three-body one of a similar form is derived. When expressed in appropriate variables, the…

The analytical formulae for the phase space factors and the three-momenta of three- and four-body final states are derived for all sets of independent kinematic variables containing invariant mass variables. These formulae will help…

In this work we study 2- and 3-body oscillators with quadratic and sextic pairwise potentials which depend on relative distances, $|{\bf r}_i - {\bf r}_j |$, between particles. The two-body harmonic oscillator is two-parametric and can be…

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for…

We present a method for solving trapped few-body problems and apply it to three equal-mass particles in a one-dimensional harmonic trap, interacting via a contact potential. By expressing the relative Hamiltonian in Jacobi cylindrical…

A method is proposed for the characterisation of the entropy of cellular structures, based on the compactivity concept for granular packings. Hamiltonian-like volume functions are constructed both in two and in three dimensions, enabling…

A brief excursion into the three-body problem in quantum mechanics is presented for graduate students or researchers in nuclear physics. Starting from single-particle coordinates, the three-body Schr\"{o}dinger equation is systematically…

The phase space of relativistic particle mechanics is defined as the 1st jet space of motions regarded as timelike 1-dimensional submanifolds of spacetime. A Lorentzian metric and an electromagnetic 2-form define naturally on the…

We present a non-variational, kinetic energy operator approach to the solution of quantum three-body problem with Coulomb interactions, based on the utilization of symmetries intrinsic to the kinetic energy operator, i.e., the three-body…

The traditional nuclear shell model approach is extended to include many-body forces. The empirical Hamiltonian with a three-body force is constructed for the identical nucleons on the 0f7/2 shell. Manifestations of the three-body force in…

We explore geometric phases of coherent states and some of their properties. A better and elegant expression of geometric phase for coherent state is derived. It is used to obtain the explicit form of the geometric phase for entangled…

We apply a symmetrization procedure to the setting of Jacobi expansions and study potential spaces in the resulting situation. We prove that the potential spaces of integer orders are isomorphic to suitably defined Sobolev spaces. Among…

The determination of the two-body density functional from its one-body density is achieved for Moshinsky's harmonium model, using a phase-space formulation, thereby resolving its phase dilemma. The corresponding sign rules can equivalently…

The problem of three different masses bound by harmonic oscillator potentials is solved exactly. It is shown that Jacobi coordinates cannot, in general, decouple this system into two three-dimensional oscillators but this decoupling can…

The four-body Yakubovsky equations in a Three-Dimensional approach with the inclusion of the three-body forces is proposed. The four-body bound state with two- and three-body interactions is formulated in Three-Dimensional approach for…

We study the phase space of spatially homogeneous and isotropic cosmology in general scalar-tensor theories. A reduction to a two-dimensional phase space is performed when possible-in these situations the phase space is usually a…

Quantum devices are preparing increasingly more complex entangled quantum states. How can one effectively study these states in light of their increasing dimensions? Phase spaces such as Wigner functions provide a suitable framework. We…

For a particular case of three-body scattering in two dimensions, and matching analytical expressions at a transition point, we obtain accurate solutions for the hyperspherical adiabatic basis and potential. We find analytical expressions…