Exactly Solvable Three-body SUSY Systems with Internal Degrees of Freedom
نویسنده
چکیده
The approach of multi-dimensional SUSY Quantum Mechanics is used in an explicit construction of exactly solvable 3-body ( and quasi-exactly-solvable N -body ) matrix problems on a line. From intertwining relations with time-dependent operators, we build exactly solvable non-stationary scalar and 2 × 2 matrix 3-body models which are time-dependent extensions of the Calogero model. Finally, we investigate the invariant operators associated to these systems.
منابع مشابه
Exact Solution to the Schrödinger Equation for the Quantum Rigid Body
The three-body problem is a fundamental problem in quantum mechanics, which has not been well solved. The Faddeev equations [1] provide a method for solving exactly the quantum three-body problems. However, only a few analytically solvable examples were found [2]. The accurate direct solution of the three-body Schrödinger equation with the separated center-of-mass motion has been sought based o...
متن کاملMutual-exclusion statistics in exactly solvable models in one and higher dimensions at low temperatures.
We study statistical characterization of the many-body states in exactly solvable models with internal degrees of freedom. The models under consideration include the isotropic and anisotropic Heisenberg spin chain, the Hubbard chain, and a model in higher dimensions which exhibits the Mott metal-insulator transition. It is shown that the ground state of these systems is all described by that of...
متن کاملThree-body Generalizations of the Sutherland Problem
The three-particle Hamiltonian obtained by replacing the twobody trigonometric potential of the Sutherland problem by a threebody one of a similar form is shown to be exactly solvable. When written in appropriate variables, its eigenfunctions can be expressed in terms of Jack symmetric polynomials. The exact solvability of the problem is explained by a hidden sl(3, R) symmetry. A generalized Su...
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 کاملAn Efficient Strain Based Cylindrical Shell Finite Element
The need for compatibility between degrees of freedom of various elements is a major problem encountered in practice during the modeling of complex structures; the problem is generally solved by an additional rotational degree of freedom [1-3]. This present paper investigates possible improvements to the performances of strain based cylindrical shell finite element [4] by introducing an additio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000