搜索结果: 1-12 共查到“物理学 Polynomial”相关记录12条 . 查询时间(0.232 秒)
Alexander Polynomial Invariants of Torus Knots T(n,3) and Chebyshev Polynomials
Alexander Polynomial Invariants Chebyshev Polynomials Mathematical Physics
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2011/9/22
Abstract: The explicit formula, which expresses the Alexander polynomials \Delta_{n,3}(t) of torus knots T(n,3) as a sum of the Alexander polynomials \Delta_{k,2}(t) of torus knots T(k,2), is found. U...
Exact polynomial solutions of second order differential equations and their applications
Polynomial solutions Bethe ansatz Quasi-exactly solvable systems
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2011/9/21
Abstract: We find all polynomials $Z(z)$ such that the differential equation $${X(z)\frac{d^2}{dz^2}+Y(z)\frac{d}{dz}+Z(z)}S(z)=0,$$ where $X(z), Y(z), Z(z)$ are polynomials of degree at most 4, 3, 2 ...
The Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem
Heine-Stieltjes correspondence polynomial approach to the standard
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2011/7/20
A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of the standard pairing problem is established based on the Heine-Stieltjes correspondence.
The Heine-Stieltjes correspondence and the polynomial approach to the standard pairing problem
The Heine-Stieltjes correspondence the polynomial the standard pairing problem Nuclear Theory
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2011/7/28
Abstract: A new approach for solving the Bethe ansatz (Gaudin-Richardson) equations of the standard pairing problem is established based on the Heine-Stieltjes correspondence. For $k$ pairs of valence...
Heun's equation, generalized hypergeometric function and exceptional Jacobi polynomial
Heun's equation generalized hypergeometric function exceptional Jacobi polynomial
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2011/7/27
Abstract: We study Heun's differential equation in the case that one of the singularities is apparent. In particular we conjecture a relationship with generalized hypergeometric differential equation ...
The SL_3 Jones polynomial of the trefoil: a case study of $q$-holonomic recursions
The SL_3 Jones polynomial $q$-holonomic recursions
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2010/12/27
The SL_3 colored Jones polynomial of the trefoil knot is a $q$-holonomic sequence of two variables with natural origin, namely quantum topology. The paper presents an explicit set of generators for th...
Physical applications of second-order linear differential equations that admit polynomial solutions
Criteria for polynomial solutions Asymptotic iteration method Confluent Heun equation Bicon-fluent Heun equation General Heun equation Davidson potential Exactly solvable differential equations
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2010/10/21
to have polynomial solutions are given. Several application of these results to Schr¨odinger’s equation are discussed. Conditions under which the confluent, biconfluent, and the general Heun equation ...
Polynomial algebras and exact solutions of general quantum non-linear optical models I: Two-mode boson systems
Polynomial algebras exact solutions quantum non-linear optical
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2010/4/2
We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use...
Coherent states, displaced number states and Laguerre polynomial states for su(1,1) Lie algebra
Coherent states displaced number states Laguerre polynomial states su(1,1) Lie algebra
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2010/10/13
The ladder operator formalism of a general quantum state for su(1,1)ie algebra is obtained. The state bears the generally deformed oscillator algebraic structure. It is found that the Perelomov’s cohe...
A Unified Model of All Generalizations from the Jones Polynomial
Jones polynomial skein relation tangle algebra recursion formula
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2007/8/15
2001Vol.35No.4pp.431-434DOI:
A Unified Model of All Generalizations from the Jones Polynomial
QIAN Shang-Wu1 and GU Zhi-Yu2
1 Department of Physics, Peking University, B...
Analytic Expression of Arbitrary Matrix Elements for Boson
Exponential Quadratic Polynomial Operators
Boson exponential quadratic polynomial operator matrix element
P representation partition function of Boson quadratic polynomial system
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2007/8/15
2007Vol.47No.1pp.41-44DOI:
Analytic Expression of Arbitrary Matrix Elements for Boson
Exponential Quadratic Polynomial Operators
XU Xiu-Wei, REN Ting-Qi, LIU Shu-Yan, MA Qiu-Ming,...
A Polynomial Expansion Method and
New General Solitary Wave Solutions to KS Equation
KS equation solitary wave solution
polynomial expansion method
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2007/8/15
2003Vol.39No.6pp.641-642DOI:
A Polynomial Expansion Method and
New General Solitary Wave Solutions to KS Equation
PENG Yan-Ze
Laboratory of Pure and Applied Mathematics,...