Solvable Two - Dimensional Schrödinger

نویسنده

  • A. P. VESELOV
چکیده

S.P.Novikov: University of Maryland at College Park, Department of Mathematics and IPST, College Park MD 20742-2431 USA and Landau Institute for Theoretical Physics, Moscow 117940, Kosygin street 2, Russia. E-mail adress [email protected] A.P.Veselov: Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK and Department of Mathematics and Mechanics, Moscow State University, 119899 Moscow Russia. E-mail adress [email protected]

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On algebraic classification of quasi-exactly solvable matrix models

We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schrödinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie a...

متن کامل

Lie algebraic approach of quasi - exactly solvable potentials with two known eigenstates

We compare two recent approaches of quasi-exactly solvable Schrödinger equations, the first one being related to finite-dimensional representations of sl(2, R) while the second one is based on supersymmetric developments. Our results are then illustra ted on the Razavy potential , the sextic oscillator and a scalar field model.

متن کامل

New approach to (quasi)-exactly solvable Schrödinger equations with a position-dependent effective mass

By using the point canonical transformation approach in a manner distinct from previous ones, we generate some new exactly solvable or quasi-exactly solvable potentials for the one-dimensional Schrödinger equation with a position-dependent effective mass. In the latter case, SUSYQM techniques provide us with some additional new potentials. PACS: 02.30.Gp, 03.65.Ge

متن کامل

Conditional symmetry and spectrum of the one-dimensional Schrödinger equation

We develop an algebraic approach to studying the spectral properties of the stationary Schrödinger equation in one dimension based on its high order conditional symmetries. This approach makes it possible to obtain in explicit form representations of the Schrödinger operator by n×n matrices for any n ∈ N and, thus, to reduce a spectral problem to a purely algebraic one of finding eigenvalues of...

متن کامل

A Super-Integrable Two-Dimensional Non-Linear Oscillator with an Exactly Solvable Quantum Analog⋆

Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky–Winternitz in two dimensions are studied and identified with motions in spaces of constant curvature, the deformation parameter being related with the curvature. In this sense these systems are to be considered as a harmonic oscillator and a Smorodins...

متن کامل

Quasi-Exactly Solvable One-Dimensional Equations

Quasi-exactly solvable one-dimensional Schrödinger equations can be specified in order to exhibit supplementary analytic eigenstates. While the usual solutions are preserved by the sl(2,R) generators, the additional ones are stabilized at the level of the universal enveloping algebra of this Lie structure. We discuss the square-integrability, the orthogonality of these supplementary solutions a...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997