Related papers: A small parameter approach for few-body problems
For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such kind of problems, we develop a general solution…
The Bethe-Peierls asymptotic approach which models pairwise short-range forces by contact conditions is introduced in arbitrary representation for spatial dimensions less than or equal to 3. The formalism is applied in various situations…
An asymptotic small parameter expansion of a single Cauchy problem is constructed for a singularly perturbed system of hyperbolic equations describing vibrations of two rigidly connected strings. Equations (such as generalized Korteweg-de…
This paper proposes a very simple perturbative technique to calculate the low-lying eigenvalues and eigenstates of a parity-symmetric quantum-mechanical potential. The technique is to solve the time-independent Schroedinger eigenvalue…
A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…
A new method is presented to reconstruct the potential of a quantum mechanical many-body system from observational data, combining a nonparametric Bayesian approach with a Hartree-Fock approximation. A priori information is implemented as a…
The new scheme employed (throughout the thermodynamic phase space), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions are formulated…
We propose two improvements to the well-known power series method for confined one-dimensional quantum-mechanical problems. They consist of the addition of a variational step were the energy plays the role of a variational parameter. We…
Base inertial parameters constitute a minimal inertial parametrization of mechanical systems that is of interest, for example, in parameter estimation and model reduction. Numerical and symbolic methods are available to determine their…
We discuss a recent test of the performance of the kinetic energy partition method (KEP) through its application to two separable quantum-mechanical models. We argue that one of the benchmark models is exceedingly simple for testing any…
In this article, I discuss the motion of $N$ point masses in non-relativistic mechanics, when the interaction between them is purely the Newtonian gravitational interaction, with $N$ greater than or equal to 2. The dynamical equations of…
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
The dominantly orbital state method allows a semiclassical description of quantum systems. At the origin, it was developed for two-body relativistic systems. Here, the method is extended to treat two-body Hamiltonians and systems with three…
The problem concerning the minimum time for an initial state to evolve up to a target state plays an important role in the Classic Optimal Control theory. In the quantum context, as quantum states are so sensitive to environmental…
The auxiliary field method is a technique to obtain approximate closed formulae for the solutions of both nonrelativistic and semirelativistic eigenequations in quantum mechanics. For a many-body Hamiltonian describing identical particles,…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
Direct approaches to the quantum many-body problem suffer from the so-called "curse of dimensionality": the number of parameters needed to fully specify the exact wavefunction grows exponentially with increasing system size. This motivates…
The study of quantum chromodynamics (QCD) over the past quarter century has had relatively little impact on the traditional approach to the low-energy nuclear many-body problem. Recent developments are changing this situation. New…
Few body methods are used in many particle physics to describe correlations, bound states, and reactions in strongly correlated quantum systems. Although this has already been recognized earlier, rigorous attempts to treat three-body…
The energy-based stochastic extension of the Schrodinger equation is a rather special nonlinear stochastic differential equation on Hilbert space, involving a single free parameter, that has been shown to be very useful for modelling the…