Related papers: Two quantum particles trapped in three dimensions …
A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights since they are often amenable to exact methods. However, no exact solution is…
We discussed exact solutions of the Schroedinger equation for a two-dimensional parabolic confinement potential in a homogeneous external magnetic field. It turns out that the two-electron system is exactly solvable in the sense, that the…
We study time evolution of Wigner function of an initially interacting one-dimensional quantum gas following the switch-off of the interactions. For the scenario where at $t=0$ the interactions are suddenly suppressed, we derive a…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
A simple system of two particles in a bidimensional configurational space $S$ is studied. The possibility of breaking in $S$ the time independent Schr\"{o}dinger equation of the system into two separated one-dimensional one-body…
The envelope theory is a reliable and easy to implement method to solve time independent Schr\"odinger-like equations (eigenvalues and eigenvectors). It is particularly useful to solve many-body systems since the computational cost is…
An outline is given how to formulate a relativistic unitarized constituent quark model of mesons in momentum space, employing harmonic quark confinement. As a first step, the momentum-space harmonic-oscillator potential is solved in a…
We show that a system consisting of two interacting particles with mass ratio $3$ or $1/3$ in a hard-wall box can be exactly solved by using Bethe-type ansatz. The ansatz is based on a finite superposition of plane waves associated with a…
In this paper we study a model of the two-dimensional quantum harmonic oscillator in a 3-dimensional anti-de Sitter background. We use a generalized Schr\"odinger picture in which the analogs of the Schr\"odinger operators of the particle…
The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant…
Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant…
The problem of two interacting particles in a quasiperiodic potential is addressed. Using analytical and numerical methods, we explore the spectral properties and eigenstates structure from the weak to the strong interaction case. More…
Quantum particles under geometric constraints are sensitive to the geometry and topology of the underlying space. We analytically study the laser-driven nonlinear dynamics of a quantum particle whose motion is constrained to a…
It is shown fields that cannot be represented over one complex plane can be further decomposed for representation over multiple complex planes. This finding is demonstrated here by solving of the Schr\"{o}dinger equation for the hydrogen…
In this work, the dynamics of quark-antiquark pair systems is investigated by modelling them as general time-dependent 3D oscillators perturbed by a Coulomb potential. Solving this model enables the prediction of key mesonic properties such…
We study the bifurcation diagram of the Onsager free-energy func- tional for liquid crystals with orientation parameter on the sphere in three dimensions. In particular, we concentrate on a very general class of two- body interaction…
We analyze scattering in a system of two (distinguishable) particles moving on the half-line $\overline{\rz}_+$ under the influence of singular two-particle interactions. Most importantly, due to the spatial localization of the interactions…
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. We solve the Schr\"odinger equation in terms of Weber functions and discuss the behavior of the eigenvalues and eigenfunctions. We derive the…
We apply the newly developed theory of permutation-symmetric O(6) hyperspherical harmonics to the quantum-mechanical problem of three non-relativistic quarks confined by a spin-independent 3-quark potential. We use our previously derived…
A novel approach for studying phase transitions in systems with quantum degrees of freedom is discussed. Starting from the microscopic hamiltonian of a quantum model, we first derive a set of exact differential equations for the free energy…