W-代数W(2,2)的单参数量子形变(英文)

众所周知,泛包络代数的量子形变所对应的量子群结构是依据所给代数的单根系给出的.我们构造了q-形变W代数Wq,并给出其非平凡的量子群结构.     

Exact solution of Schrdinger equation with q-deformed quantum potentials using Nikiforov–Uvarov method

In this paper,we present the exact solution of the one-dimensional Schrdinger equation for the q-deformed quantum potentials via the Nikiforov–Uvarov method.The eigenvalues and eigenfunctions of these potentials are obtained via this method.The energy equations and the corresponding wave functions for some special cases of these potentials are briefly discussed.The PT-symmetry and Hermiticity for these potentials are also discussed.     

均匀电场中D维q变形带电振子的双波描述

应用双波理论描述均匀电场中D维q变形带电振子的运动,得到了振子各力学量随时间的演化方程.     

Algebraic Model Applied to Vibrations in the Electronic Ground State of NO2

An algebraic model of boson realization and a corresponding q-deformed model are used to study tile vibrations in the electronic ground state of NO₂. The two models are applied to fit the 142 vibrational band origins below 9000 cm^-1 with the standard deviations 3.23 cm^-1 and 3.12 cm^-1, respectively.     

Automorphisms of the q-deformed algebra suq(1, 1) and d-Orthogonal polynomials of q-Meixner type

Starting from an operator given as a product of q-exponential functions in irreducible representations of the positive discrete series of the q-deformed algebra su_q(1, 1), we express the associated matrix elements in terms of d-orthogonal polynomials. An algebraic setting allows to establish some properties : recurrence relation, generating function, lowering operator, explicit expression and d-orthogonality relations of the involved polynomials which are reduced to the orthogonal q-Meixner polynomials when d=1. If q ↑ 1, these polynomials tend to some d-orthogonal polynomials of Meixner type.     

Eigen spectra and wave functions of the massless Dirac fermions under the nonuniform magnetic fields in graphene

In this research, firstly, by using the new form of Dirac-Weyl equation and the series method with submitting more suitable details, the energy spectrum and wave functions of the massless Dirac fermions are calculated under the inhomogeneous and q-deformed spatially magnetic fields. Although, we discussed about the results of the energy levels, further, we obtained the wave function as the Hessenberg determinant with calculating the elements of it as exact. On the other hand, by using the Mellin-Barnes integral representation and Hurwitz zeta function, we have achieved the thermodynamic physical quantities of the Dirac-Weyl fermions in the absence of a magnetic field for inside of the graphene quantum dot. Finally, our numerical results for the wave functions and probability densities are presented too.     

Approximate ℓ-bound state solutions of q-deformed exponential-type potentials

In this work, the exactly solvable Schrödinger equation for s-states of a class of multiparameter exponential-type potential (E-tP) is used to obtain the approximate ℓ ≠ 0 bound state solutions for the corresponding q-deformed radial potentials. To deal with the effective potential, the Pekeris approximation for the centrifugal term is applied. The proposal has the advantage that, depending on the choice of the parameters involved in the E-tP, several q-deformed exponential potentials are obtained here as particular cases. That is, our proposition indicates that it is not necessary to use specialized methods to solve the Schrödinger equation for specific q-deformed exponential potentials. At this regard, in order to show the usefulness of the proposed method, we consider the ℓ ≠ 0 bound state solutions of the q-deformed Tietz, Hulthén, Manning-Rosen, Shioberg, quadratic exponential, Wei and Hua among other potential models. Furthermore, with the example of the Hua potential we are contributing to solve the recent controversy on the energy spectra of this q-deformed model. Moreover, in some applications considered in this work the results can be used to correct similar findings already published. Besides, the proposal is useful when considering new q-deformed potentials with hypergeometric wavefunctions to be used in quantum chemical applications of diatomic molecules.     

q形变光场与级联型三能级原子相互作用中场的压缩效应

建立了q形变光场与级联型三能级原子相互作用的非线性理论,求得相互作用绘景中薛定谔方程的形式解,利用数值计算讨论了q形变对相互作用中场压缩效应的影响并与q-偶相干光场的情形做了对比分析。研究发现,q偏离1的程度越大,q形变对场压缩效应的调控能力越强,反映出q形变的非线性行为对量子相干性的干扰以及对量子特性的影响。当q→1时,恢复为普通线性理论。和q-偶相干光场的情形做的对比分析,反映出q-奇相干光场不仅不存在压缩效应,还会弱化压缩效应。这与q-偶相干光场和q-奇相干光场存在不同的量子效应的结论完全一致。     

Exact peakon solutions given by the generalized hyperbolic functions for some nonlinear wave equations

In 1993, Camassa and Holm drived a shallow water equation and found that this equation has a peakon solution with the form $\phi(\xi)=ce^{-|\xi|}$. In this paper, we show that three nonlinear wave systems have peakon solutions which needs to be represented as generalized hyperbolic functions. For the existence of these solutions, some constraint parameter conditions are derived.