Supersymmetry, Shape Invariance and Solvability of AN−1 and BCN Calogero-Sutherland Model
نویسندگان
چکیده
Using the ideas of supersymmetry and shape invariance we re-derive the spectrum of the AN−1 and BCN Calogero-Sutherland model. We briefly discuss as to how to obtain the corresponding eigenfunctions. We also discuss the difficulties involved in extending this approach to the trigonometric models. PACS numbers: 03.65.Ge, 05.30.-d Typeset using REVTEX 1 Electronic address: [email protected] 2 Electronic address:[email protected] 3 Electronic address:[email protected] 1
منابع مشابه
Super-Calogero-Moser-Sutherland systems and free super-oscillators : a mapping
We show that the supersymmetric rational Calogero-Moser-Sutherland (CMS) model of AN+1-type is equivalent to a set of free super-oscillators, through a similarity transformation. We prescribe methods to construct the complete eigen-spectrum and the associated eigen-functions, both in supersymmetry preserving as well as supersymmetry breaking phases, from the free super-oscillator basis. Further...
متن کاملShape Invariance in the Calogero and Calogero-Sutherland Models
We show that the Calogero and Calogero-Sutherland models possess an N -body generalization of shape invariance. We obtain the operator representation that gives rise to this result, and discuss the implications of this result, including the possibility of solving these models using algebraic methods based on this shape invariance. Our representation gives us a natural way to construct supersymm...
متن کاملHidden Algebras of the (super) Calogero and Sutherland models
We propose to parametrize the configuration space of one-dimensional quantum systems of N identical particles by the elementary symmetric polynomials of bosonic and fermionic coordinates. It is shown that in this parametrization the Hamiltonians of the AN , BCN , BN , CN and DN Calogero and Sutherland models, as well as their supersymmetric generalizations, can be expressed — for arbitrary valu...
متن کاملIntegrable 1/r Spin Chain with Reflecting End
A new integrable spin chain of the Haldane-Shastry type is introduced. It is interpreted as the inverse-square interacting spin chain with a reflecting end. The lattice points of this model consist of the square of the zeros of the Laguerre polynomial. Using the “exchange operator formalism”, the integrals of motion for the model are explicitly constructed. Typeset using REVTEX ∗E-mail address ...
متن کاملB N - type Dunkl operators
We construct several new families of exactly and quasi-exactly solvable BCN -type Calogero– Sutherland models with internal degrees of freedom. Our approach is based on the introduction of a new family of Dunkl operators of BN type which, together with the original BN -type Dunkl operators, are shown to preserve certain polynomial subspaces of finite dimension. We prove that a wide class of qua...
متن کامل