Imprimitively Generated Lie-Algebraic Hamiltonians and Separation of Variables
نویسندگان
چکیده
منابع مشابه
Imprimitively Generated Lie-algebraic Hamiltonians and Separation of Variables
Turbiner’s conjecture posits that a Lie-algebraic Hamiltonian operator whose domain is a subset of the Euclidean plane admits a separation of variables. A proof of this conjecture is given in those cases where the generating Lie-algebra acts imprimitively. The general form of the conjecture is false. A counter-example is given based on the trigonometric OlshanetskyPerelomov potential correspond...
متن کاملNon-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
We show that complex Lie algebras (in particular sl(2,C)) provide us with an elegant method for studying the transition from real to complex eigenvalues of a class of non-Hermitian Hamiltonians: complexified Scarf II, generalized Pöschl-Teller, and Morse. The characterizations of these Hamiltonians under the so-called pseudoHermiticity are also discussed. PACS: 02.20.Sv; 03.65.Fd; 03.65.Ge
متن کاملLie Algebras, Algebraic Groups, and Lie Groups
These notes are an introduction to Lie algebras, algebraic groups, and Lie groups in characteristic zero, emphasizing the relationships between these objects visible in their categories of representations. Eventually these notes will consist of three chapters, each about 100 pages long, and a short appendix. Single paper copies for noncommercial personal use may be made without explicit permiss...
متن کاملLie Algebras of Differential Operators and Lie-Algebraic Potentials
An explicit characterisation of all second order differential operators on the line which can be written as bilinear combinations of the generators of a linitedimensional Lie algebra of first order differential operators is found, solving a problem arising in the Lie-algebraic approach to scattering theory and molecular dynamics. One-dimensional potentials corresponding to these Lie algebras ar...
متن کاملLie algebraic Noncommutative Gravity
We exploit the Seiberg – Witten map technique to formulate the theory of gravity defined on a Lie algebraic noncommutative space time. Detailed expressions of the Seiberg – Witten maps for the gauge parameters, gauge potentials and the field strengths have been worked out. Our results demonstrate that notwithstanding the introduction of more general noncommutative structure there is no first or...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Canadian Journal of Mathematics
سال: 1998
ISSN: 0008-414X,1496-4279
DOI: 10.4153/cjm-1998-063-2