Anharmonic oscillators, spectral determinant and short exact sequence of
نویسندگان
چکیده
منابع مشابه
Anharmonic Oscillators, Spectral Determinant and Short Exact Sequence of U Q ( Sl 2 )
We prove one of conjectures, raised by Dorey and Tateo in the connection among the spectral determinant of anharmonic oscillator, vacuum eigenvalues of transfer matrices in field theory and statistical mechanics. The exact sequence of Uq(ŝl2) plays a fundamental role in the proof. ∗e-mail: [email protected]
متن کاملOn Exact Solvability of Anharmonic Oscillators in Large Dimensions
Abstract. General Schrödinger equation is considered with a central polynomial potential depending on 2q arbitrary coupling constants. Its exceptional solutions of the so called Magyari type (i.e., exact bound states proportional to a polynomial of degree N) are sought. In any spatial dimension D ≥ 1, this problem leads to the Magyari’s system of coupled polynomial constraints, and only purely ...
متن کاملNew Type of Exact Solvability and of a Hidden Nonlinear Dynamical Symmetry in Anharmonic Oscillators
Schrödinger bound-state problem in D dimensions is considered for a set of central polynomial potentials containing 2q arbitrary coupling constants. Its polynomial (harmonicoscillator-like, quasi-exact, terminating) bound-state solutions of degree N are sought at an (q + 1)-plet of exceptional couplings/energies, the values of which comply with (the same number of) termination conditions. We re...
متن کاملZeros of eigenfunctions of some anharmonic oscillators
where P is a real even polynomial with positive leading coefficient, which is called a potential. The boundary condition is equivalent to y ∈ L(R) in this case. It is well-known that the spectrum is discrete, and all eigenvalues λ are real and simple, see, for example [3, 14]. The spectrum can be arranged in an increasing sequence λ0 < λ1 < . . .. Eigenfunctions y are real entire functions of o...
متن کاملSextic 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 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: Journal of Physics A: Mathematical and General
سال: 1999
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/32/16/002