2003/02/18 by N. Gurappa, Prasanta K. Panigrahi
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #cond-mat
paper · pdf · doi:10.1103/physrevb.67.155323
18 pages, Revtex format, To appear in Physical Review B
arxiv created 2003/02/18 · openalex publication_date 2003/04/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The present paper is an extended version of another paper [Phys. Rev. B 59, R2490 (1999)], where we have established the equivalence of the Calogero-Sutherland model to decoupled oscillators. Here, we first employ the same approach for finding the eigenstates of a large class of Hamiltonians, dealing with correlated systems. A number of few- and many-body interacting models are studied and the relationship between their respective Hilbert spaces, with that of oscillators, is found. This connection is then used to obtain the spectrum generating algebras for these systems and make an algebraic statement about correlated systems. The procedure to generate solvable interacting models is outlined. We then point out the inadequacies of the present technique and make use of a method for solving linear differential equations to diagonalize the Sutherland model and establish a precise connection between this correlated system's wave functions, with those of the free particles on a circle. In the process, we obtain an expression for the Jack polynomials. In two dimensions, we analyze the Hamiltonian having Laughlin wave function as the ground state and point out the natural emergence of the underlying linear W_1+\ensuremath∞ symmetry in this approach.