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Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…

Precise variational solutions are given for problems involving diverse fermionic and bosonic $N=2-7$-body systems. The trial wave functions are chosen to be combinations of correlated Gaussians, which are constructed from products of the…

The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…

Newton's equations of celestial mechanics are shown to possess a continuum of solutions in which the future trajectories of the N bodies are a perfect reflection of their past. These solutions evolve from zero initial velocities of the N…

We derive rigorously, for both R^2 and [-L, L]^2, the cubic nonlinear Schrodinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair interactions. We first prove convergence…

We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…

Dynamics in correlated quantum matter is a hard problem, as its exact solution generally involves a computational effort that grows exponentially with the number of constituents. While a remarkable progress has been witnessed in recent…

It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…

We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length.Two-body problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for…

In the reversible Schrodinger-Newton equation a complex Newton coupling G*exp(-i*alpha) is proposed in place of G. The equation becomes irreversible and all initial one-body states are expected to converge to solitonic stationary states.…

We study central configurations in the four body problem, i.e., configurations in which the forces on all the bodies point to a fixed, single point in space. The newly formulated pair-space formalism yields a set of vectorial equations that…

Various many-body models are treated, which describe $N$ points confined to move on a plane circle. Their Newtonian equations of motion ("accelerations equal forces") are integrable, i. e. they allow the explicit exhibition of $N$ constants…

The toy model of a particle on a vertical rotating circle in the presence of uniform gravitational/ magnetic fields is explored in detail. After an analysis of the classical mechanics of the problem we then discuss the quantum mechanics…

We study the bifurcations of central configurations of the Newtonian four-body problem when some of the masses are equal. First, we continue numerically the solutions for the equal mass case, and we find values of the mass parameter at…

Real-time computation of time-dependent quantum mechanical problems are presented for nuclear many-body problems. Quantum tunneling in nuclear fusion at low energy is described using a time-dependent wave packet. A real-time method of…

By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional Schr\"odinger equation with a…

A supersymmetric technique for the solution of the effective mass Schr\"{o}% dinger equation is proposed. Exact solutions of the Schroedinger equation corresponding to a number of potentials are obtained. The potentials are fully…

Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum…

A new form of quasiclassical space-time dynamics for constrained systems reveals how quantum effects can be derived systematically from canonical quantization of gravitational systems. These quasiclassical methods lead to additional fields,…

The classical behaviour of a macroscopic system consisting of a large number of microscopic systems is derived in the framework of the Bohmian interpretation of quantum mechanics. Under appropriate assumptions concerning the localization…