Test of a general symmetry-derived N -body wave function

The resources required to solve the general interacting quantum N-body problem scale exponentially with N, making the solution of this problem very difficult when N is large. In a previous series of papers we develop an approach for a fully interacting wave function for a confined system of identica...

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Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2009-12, Vol.80 (6), Article 062108
Main Authors: Dunn, Martin, Laing, W. Blake, Toth, Derrick, Watson, Deborah K.
Format: Article
Language:English
Subjects:
ATOMIC AND MOLECULAR PHYSICS
BOSONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COMPARATIVE EVALUATIONS
CONVERGENCE
DISTURBANCES
EVALUATION
FUNCTIONS
GROUP THEORY
INTERACTING BOSON MODEL
MANY-BODY PROBLEM
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS
MATHEMATICS
MECHANICS
NUCLEAR MODELS
PERTURBATION THEORY
QUANTUM MECHANICS
SHELL MODELS
TWO-BODY PROBLEM
WAVE FUNCTIONS
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Summary:The resources required to solve the general interacting quantum N-body problem scale exponentially with N, making the solution of this problem very difficult when N is large. In a previous series of papers we develop an approach for a fully interacting wave function for a confined system of identical bosons with a general two-body interaction. This method tames the N scaling by developing a perturbation series that is order-by-order invariant under a point group isomorphic with S{sub N}. Group theory and graphical techniques are then used to solve for the wave function exactly and analytically at each order, yielding a solution for the general N-body problem which scales as N{sup 0} at any given order. Recently this formalism has been used to obtain the first-order fully interacting wave function for a system of harmonically confined bosons interacting harmonically. In this paper, we report the application of this N-body wave function to a system of N fully interacting bosons in three dimensions. We derive an expression for the density profile for a confined system of harmonically interacting bosons. Choosing this simple interaction is not necessary or even advantageous for our method, however this choice allows a direct comparison of our exact results through first order with exact results obtained in an independent solution. Our density profile for the wave function through first order in three dimensions is indistinguishable from the first-order exact result obtained independently and shows strong convergence to the exact result to all orders.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.80.062108