Related papers: Two-body quantum mechanical problem on spheres
A duality between an electrostatic problem in a three dimensional world and a quantum mechanical problem in a one dimensional world which allows one to obtain the ground state solution of the Schr\"odinger equation by using electrostatic…
A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.
A nonlinear model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature is exactly solved. This model depends of a parameter $\la$ that is related with the curvature of the space. Firstly the relation with other…
Free classical particles have well-defined momentum and position, while free quantum particles have well-defined momentum but a position fully delocalized over the sample volume. We develop a many-body formalism based on wave-packet…
A method of solving the Schr\"{o}dinger equation based on the use of constant particle-particle interaction potential surfaces (IPS) is proposed. The many-body wave function is presented in a configuration interaction form, with…
Equation of motion of Sommerfeld sphere in the field of Coulomb center is numerically investigated. It is shown that contrary to Lorentz-Dirac equation in the attractive case there are physical solutions. In the repulsive case sphere gains…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
We review the recently proposed unreduced, complex-dynamical solution to the many-body problem with arbitrary interaction and its application to the unified solution of fundamental problems, including dynamic foundations of causally…
An analytical solution of the quantum problem of an electron on a spherical segment with angular confinement potential of the form of rectangular impenetrable walls is presented. It is shown that the problem is reduced to finding solution…
We employ generalized Euler coordinates for the $n$ body system in $d \geq n-1$ dimensional space, which consists of the centre-of-mass vector, relative (mutual), mass-independent distances $r_{ij}$ and angles as remaining coordinates. We…
Non-equilibrium thermodynamics can provide strong advantages when compared to more standard equilibrium situations. Here, we present a general framework to study its application to concrete problems, which is valid also beyond the…
Systems built out of N-body interactions, beyond 2-body interactions, are formulated on the plane, and investigated classically and quantum mechanically (in phase space). Their Wigner Functions--the density matrices in phase-space…
We review our recent work addressing various theoretical issues in spin-based quantum dot quantum computation and quantum information processing. In particular, we summarize our calculation of electron exchange interaction in two-electron…
We give a self-contained presentation and comparison of two different algorithms to explicitly solve quantum many body models of indistinguishable particles moving on a circle and interacting with two-body potentials of $1/\sin^2$-type. The…
We solve the quantum mechanical problem of a charged particle on S^2 in the background of a magnetic monopole for both bosonic and supersymmetric cases by constructing Hilbert space and realizing the fundamental operators obeying…
A non-perturbative renormalization of a many-body problem, where non-relativistic bosons living on a two dimensional Riemannian manifold interact with each other via the two-body Dirac delta potential, is given by the help of the heat…
We study the properties of two quantum particles which are confined in a ring. The particles interact via a long-range gauge potential proportional to the distance between the particles. It is found that the two-body ground state…
In the present work, we present different two-body potentials which have oscillatory shapes with magnetic interactions. The eigenvalues and eigenfunctions are obtained for one of those problems using Nikiforov-Uvarov method.
The non-commutativity of the position and momentum operators is formulated as an effective potential in classical phase space and expanded as a series of successive many-body terms, with the pair term being dominant. A non-linear partial…