Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Many-body Schroedinger equation in the collective variables

A.K. Petrauskas, L.Yu. Sabalyauskas

Published Oct 1, 1974• 0 citations
OpenAlex

Related papers

Many-Body Schrödinger Equation

Hiroshi Isozaki

Mathematical physics studies•Jan 1, 2023•6 citations

Separation of the normal and the superfluid motions in the Schroedinger equation by means of the displacement and collective variables method

I. O. Vakarchuk, I.R. Yukhovskii

With the aid of the displacement method, the wave function of interacting bosons is represented as a product of the ground state function and the function describing the excitations in the system. The equations for these functions are solved in the collective variables representation by means of a special perturbation method free of divergences. The expressions obtained for the wave functions, the energy of the ground state, the energy spectrum and the damping of collective excitations are investigated. (auth)

•Jan 1, 1974•0 citations

Solution of the Schrödinger Equation for Many-Particle Systems

A. P. Machil'skii

SPhD•May 1, 1969•0 citations

Quantum Systems Obeying to Generalized Exclusion-Inclusion Principle

Antonio Maria Scarfone

In this work is studied a many body system obeying to a generalized Exclusion-Inclusion Principle (EIP) originated by collective effect, the dynamics, in mean field approximation, being ruled by a nonlinear Schroedinger equation. The EIP is introduced by a judicious generalization of the particle current. By means of variational principle is obtained a canonical nonlinear Schroedinger equation. We study the Lagrangian and Hamiltonian formulation. We study the symmetries of the nonlinear Schroedinger equation obeying to EIP and by means of Noether theorem we obtain and discuss conserved quantities. Successively, EIP-Schroedinger equation is coupled in a minimal way to an abelian gauge field which dynamics is described by the Maxwell-Chern-Simons Lagrangian. We show that the anyonic statistic behavior ascribed to the system by the Chern-Simons Lagrangian is not destroyed by the presence of EIP potential. Finally, we study special solutions of the system. Applications on the Bose-Einstein condensation and vortex-like solution in the picture of Chern-Simons interaction are considered.

arXiv:cond-mat/0002462•Feb 29, 2000•0 citations

Collective Behavior of the Closed-Shell Fermi Gas

Seth T. Rittenhouse, M. J. Cavagnero, Javier von Stecher +1 more

We propose an unconventional description for the ground state and collective oscillations of the two-component normal Fermi gas with two-body zero-range interactions. The many-body problem can be accurately reduced to a linear, one-dimensional Schroedinger equation in a single collective coordinate, the hyperradius R of the N-atom system which is the root mean square radius. The calculated properties of the Fermi gas ground state are shown to agree accurately with results from the Hartree-Fock (HF) approximation over a wide range of interspecies scattering lengths. The breathing mode excitation frequency deviates qualitatively from HF predictions, but we show that this reflects a failure of the HF approach for this observable.

arXiv:cond-mat/0510454•Oct 17, 2005•0 citations

Elementary Aspects of the Quantum-Mechanical Many-Body Problem

Walter Greiner

Springer eBooks•Jan 1, 2001•1 citation
With the aid of the displacement method, the wave function of interacting bosons is represented as a product of the ground state function and the function describing the excitations in the system. The equations for these functions are solved in the collective variables representation by means of a special perturbation method free of divergences. The expressions obtained for the wave functions, the energy of the ground state, the energy spectrum and the damping of collective excitations are investigated. (auth)
In this work is studied a many body system obeying to a generalized Exclusion-Inclusion Principle (EIP) originated by collective effect, the dynamics, in mean field approximation, being ruled by a nonlinear Schroedinger equation. The EIP is introduced by a judicious generalization of the particle current. By means of variational principle is obtained a canonical nonlinear Schroedinger equation. We study the Lagrangian and Hamiltonian formulation. We study the symmetries of the nonlinear Schroedinger equation obeying to EIP and by means of Noether theorem we obtain and discuss conserved quantities. Successively, EIP-Schroedinger equation is coupled in a minimal way to an abelian gauge field which dynamics is described by the Maxwell-Chern-Simons Lagrangian. We show that the anyonic statistic behavior ascribed to the system by the Chern-Simons Lagrangian is not destroyed by the presence of EIP potential. Finally, we study special solutions of the system. Applications on the Bose-Einstein condensation and vortex-like solution in the picture of Chern-Simons interaction are considered.
We propose an unconventional description for the ground state and collective oscillations of the two-component normal Fermi gas with two-body zero-range interactions. The many-body problem can be accurately reduced to a linear, one-dimensional Schroedinger equation in a single collective coordinate, the hyperradius R of the N-atom system which is the root mean square radius. The calculated properties of the Fermi gas ground state are shown to agree accurately with results from the Hartree-Fock (HF) approximation over a wide range of interspecies scattering lengths. The breathing mode excitation frequency deviates qualitatively from HF predictions, but we show that this reflects a failure of the HF approach for this observable.