Related papers: Solving Single and Many-body Quantum Problems: A N…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrodinger equation cannot be solved analytically for more than two particles. One has to resort to approximation…
Quantum hadrodynamics (QHD) is a framework for describing the nuclear many-body problem as a relativistic system of baryons and mesons. Motivation is given for the utility of such an approach and for the importance of basing it on a local,…
A surprising "duality" of the Newton equation with time-dependent forces and the stationary Schroedinger equation is discussed. Wide classes of exact solutions not known before for few-body Newton equations are generated directly from…
We introduce variational methods for finding approximate eigenfunctions and eigenvalues of quantum Hamiltonians by constructing a set of orthogonal wave functions which approximately solve the eigenvalue equation.
We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new…
Representation of the quantum measurement with the help of non-orthogonal decomposition of unit is presented in the paper for the first time. Methods for solution of the quantum detection and measurement problems based on the suggested…
Many-body systems, such as electrons flowing in a superconductor, are among the most difficult theoretical problems to study. A new family of exactly solvable models may offer some answers.
The three-body problem in one-dimension with a repulsive inverse square potential between every pair was solved by Calogero. Here, the known results of supersymmetric quantum mechanics are used to propose a number of new three-body…
We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. We…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
We propose a systematic method to construct quasi-solvable quantum many-body systems having permutation symmetry. By the introduction of elementary symmetric polynomials and suitable choice of a solvable sector, the algebraic structure of…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
This work is concerned with multi-dimensional integrals, which are making their appearance in few-body atomic and nuclear physics. It is shown that the relevant two- and three-dimensional integrals can be reduced to one-dimensional form.…
We study aspects of the quantum and classical dynamics of a $3$-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of…
A formalism is presented that allows an asymptotically exact solution of non-relativistic and semi-relativistic two-body problems with infinitely rising confining potentials. We consider both linear and quadratic confinement. The additional…
Explicit examples of quasi-exactly-solvable $N$-body problems on the line are presented. These are related to the hidden algebra $sl_N$, and they are of two types -- containing up to $N$ (infinitely-many eigenstates are known, but not all)…