Orthogonal polynomials and deformed oscillators
نویسندگان
چکیده
منابع مشابه
Sextic anharmonic oscillators and orthogonal polynomials
Under certain constraints on the parameters a, b and c, it is known that Schrödinger’s equation −d2ψ/dx2 + (ax + bx + cx)ψ = Eψ, a > 0 with the sextic anharmonic oscillator potential is exactly solvable. In this article we show that the exact wave function ψ is the generating function for a set of orthogonal polynomials {P (t) n (x)} in the energy variable E. Some of the properties of these pol...
متن کاملq-deformed dynamics of q-deformed oscillators
We show that an infinite set of q-deformed relevant operators close a partial q-deformed Lie algebra under commutation with the Arik-Coon oscillator. The dynamics is described by the multicommutator: [Ĥ, . . . , [Ĥ, Ô] . . .], that follows a power law which leads to a dynamical scaling. We study the dynamics of the Arik-Coon and anharmonic oscillators and analyze the role of q and the other par...
متن کاملSymmetric Orthogonal Polynomials and the Associated Orthogonal L-polynomials
We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained. Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx2)(l x2)~1/2, k>0.
متن کاملQuasi-exactly Soluble Potentials and Deformed Oscillators
It is proved that quasi-exactly soluble potentials corresponding to an oscillator with harmonic, quartic and sextic terms, for which the n + 1 lowest levels of a given parity can be determined exactly, may be approximated by WKB equivalent potentials corresponding to deformed anharmonic oscillators of SUq(1,1) symmetry, which have been used for the description of vibrational spectra of diatomic...
متن کاملq-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations
Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebras and root vectors and which make it possible to construct representations by operators acting according to Gel’fand–Tsetlin-type formulas. Unitary representations of the q-deformed algebras Uq(son,1) are found. AMS subject classifications (1980). 16...
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: Theoretical and Mathematical Physics
سال: 2015
ISSN: 0040-5779,1573-9333
DOI: 10.1007/s11232-015-0350-7