Algebraic treatment of the Bateman Hamiltonian
نویسندگان
چکیده
We apply the algebraic method to Bateman Hamiltonian and obtain its natural frequencies ladder operators from adjoint or regular matrix representation of that operator. Present analysis shows eigenfunctions compatible with complex eigenvalues obtained earlier by other authors are not square integrable. In addition this, annihilate an infinite number such eigenfunctions.
منابع مشابه
An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system
In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...
متن کاملAlgebraic Hamiltonian Actions
In this paper we deal with a Hamiltonian action of a reductive algebraic group G on an irreducible normal affine Poisson variety X . We study the quotient morphism μG,X//G : X//G → g//G of the moment map μG,X : X → g. We prove that for a wide class of Hamiltonian actions (including, for example, actions on generically symplectic varieties) all fibers of the morphism μG,X//G have the same dimens...
متن کاملThe Complex Bateman Equation
The general solution to the Complex Bateman equation is constructed. It is given in implicit form in terms of a functional relationship for the unknown function. The known solution of the usual Bateman equation is recovered as a special case. e-mail: [email protected] e-mail: [email protected].
متن کاملCombinatorial Invariants of Algebraic Hamiltonian Actions
To any Hamiltonian action of a reductive algebraic group G on a smooth irreducible symplectic variety X we associate certain combinatorial invariants: Cartan space, Weyl group, weight and root lattices. For cotangent bundles these invariants essentially coincide with those arising in the theory of equivarant embeddings. Using our approach we establish some properties of the latter invariants.
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 Physics
سال: 2021
ISSN: ['0008-4204', '1208-6045']
DOI: https://doi.org/10.1139/cjp-2020-0219