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Harmony in many-particle quantum problem

Константин Владимирович Чукбар

Uspekhi Fizicheskih NaukJun 1, 20172 citations

The system of harmonically interacting particles: An exact solution of the quantum‐mechanical problem

M. S. Osadchii, V. V. Murakhtanov

Abstract An original procedure has been developed to determine the eigenvalues and the eigenfunctions of quantum‐mechanical many‐body systems with a harmonic oscillator interaction. Exact solutions in the explicit form have been obtained for the case of systems containing three groups of identical particles. For the system containing two groups of identical particles, a solution in the adiabatic approximation has been obtained and compared with the exact one.

International Journal of Quantum ChemistryFeb 1, 199114 citations

The complete exact solution to the translation-invariant N-body harmonic oscillator problem

Richard L. Hall, Bernd Schwesinger

It is shown that Schrödinger’s nonrelativistic equation for a translation-invariant system of N particles with arbitrary masses interacting by harmonic pair potentials with arbitrary coupling constants is exactly soluble. An explicit matrix KV is given whose eigenvalues and eigenvectors determine all the exact energies and corresponding eigenfunctions of the N-particle problem. The result is extended to include systems composed of an arbitrary number of groups of identical particles.

Journal of Mathematical PhysicsDec 1, 197922 citations

The exact solution of theN-particle schrödinger equation with two-particle harmonic interactions

H. Almström

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoJun 1, 19694 citations

Complementary pictures of theN-boson problem

Richard L. Hall

We consider a system of N identical bosons which interact in one dimension via attractive pair potentials and obey nonrelativistic quantum mechanics. This system is studied from two complementary viewpoints. The equivalent two-body method approximates the system as a collection of (N-1) independent two-particle systems with coupling constants enhanced by the factor N/2, and this yields energy lower bounds. The collective-field method approaches the problem from the standpoint of the limit as N\ensuremath{\rightarrow}\ensuremath{\infty} and leads to energy upper bounds. We find that Gaussian trial functions for the N-particle Hamiltonian and Gaussian trial densities in the collective-field theory lead to precisely the same energy upper bounds. The upper bounds provided by field theory allow for systematic improvement via a variational principle. Details are worked out for two exactly soluble problems, namely, the harmonic oscillator and the attractive \ensuremath{\delta} potential.We consider a system of N identical bosons which interact in one dimension via attractive pair potentials and obey nonrelativistic quantum mechanics. This system is studied from two complementary viewpoints. The equivalent two-body method approximates the system as a collection of (N-1) independent two-particle systems with coupling constants enhanced by the factor N/2, and this yields energy lower bounds. The collective-field method approaches the problem from the standpoint of the limit as N\ensuremath{\rightarrow}\ensuremath{\infty} and leads to energy upper bounds. We find that Gaussian trial functions for the N-particle Hamiltonian and Gaussian trial densities in the collective-field theory lead to precisely the same energy upper bounds. The upper bounds provided by field theory allow for systematic improvement via a variational principle. Details are worked out for two exactly soluble problems, namely, the harmonic oscillator and the attractive \ensuremath{\delta} potential.

Physical Review AApr 1, 19886 citations

EXACT SOLUTIONS TO THE N-BODY SCHRÖDINGER EQUATION FOR THE HARMONIC OSCILLATOR

Zhong-Qi Ma

Foundations of Physics LettersApr 1, 20009 citations

Harmony in a many-particle quantum problem

Abstract

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Harmony in a many-particle quantum problem

Abstract

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