Theoretical Study of Optically Pumped NH3 Far-Infrared Laser in Vibrational Ground State

In this paper, the density matrix equation of three-level system for far-infrared (FIR) Raman transition in vibrational ground state was solved. By means of iteration method and numerical calculation, the spectral characteristics of NH₃ molecules FIR laser with TEA CO₂-10R(14) laser pumping was studied theoretically. The theoretical result would help us to understand the physical mechanism of optically pumped molecular gases FIR laser with ground-state reversal transition.     

A basis function for approximation and the solutions of partial differential equations

In this article, we introduce a type of basis functions to approximate a set of scattered data. Each of the basis functions is in the form of a truncated series over some orthogonal system of eigenfunctions. In particular, the trigonometric eigenfunctions are used. We test our basis functions on recovering the well‐known Franke's and Peaks functions given by scattered data, and on the extension of a singular function from an irregular domain onto a square. These basis functions are further used in Kansa's method for solving Helmholtz‐type equations on arbitrary domains. Proper one level and two level approximation techniques are discussed. A comparison of numerical with analytic solutions is given. The numerical results show that our approach is accurate and efficient. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Spin-coupled calculations based on projected spin eigenfunctions

It is outlined how the utilization of a basis of projected spin eigenfunctions can lead to increased computational efficiency in the evaluation of matrix elements and density matrices in spin-coupled valence bond calculations. Received: 17 September 1997 / Accepted: 23 October 1997     

A sturm-liouville problem with physical and spectral parameters in boundary conditions

We study the spectral probleml(u)=−u″+q(x)u(x)=λu(x),u′(0)=0, u′(π)=mλu(π), where λ andm are a spectral and a physical parameter. Form<0, we associate with the problem a self-adjoint operator in Pontryagin space II₁. Using this fact and developing analytic methods of the theory of Sturm-Liouville operators, we study the dynamics of eigenvalues and eigenfunctions of the problems asm→−0. Translated fromMatematicheskie Zametki, Vol. 66, No. 2, pp. 163–172, August, 1999.     

本征函数法求解光强传输方程的相位反演方法

提出了一种采用本征函数法求解光强传输方程的相位反演算法.相位可由拉普拉斯算子本征函数展开,各阶本征函数的系数可以由光强沿光轴的微分和本征函数两者的积分得到,由此实现相位恢复.给出了圆形区域和矩形区域拉普拉斯算子本征函数的解析形式,数值模拟了在这两种区域上采用该算法实现相位恢复的过程,结果表明该算法可以很好地实现相位恢复...     

One-dimensional Schrödinger operator on the half-line: The differential equation for eigenfunctions with respect to the spectral parameter and an analog of the Freud equation

It is shown that the eigenfunctions of the Schrödinger operator on the half-line satisfy an explicitly constructed differential equation with respect to the spectral parameter. Such an equation was earlier obtained for orthogonal polynomials. An analog of the Freud equation is found.     

Exact solution of the Klein‐Gordon equation for the PT‐symmetric generalized Woods‐Saxon potential by the Nikiforov‐Uvarov method

The exact solution of the one‐dimensional Klein‐Gordon equation of the ????‐symmetric generalized Woods‐Saxon potential is obtained. The exact energy eigenvalues and wavefunctions are derived analytically by using the Nikiforov and Uvarov method. In addition, the positive and negative exact bound states of the s‐states are also investigated for different types of complex generalized Woods‐Saxon potentials.     

Phase transitions in electron systems with short-range pairing interactions: Ground state

We propose a real-space, tight-binding model of electrons with short-range pairing interactions. The model involves a competition between the ordinary single particle hoppingt and an attractive interactionV between the singlet electronic pairs formed on neighboring lattice sites. The Hamiltonian effectively describes a mechanism for pair formation. We study the ground-state properties of its onedimensional version using numerically exact finite chain calculations for up toN= 10 sites. The ground-state wave functions, the energy spectrum, and various ground-state correlation functions are calculated with the help of an exactly equivalent system of two coupledS=1/2 spin chains. The results indicate the existence of a transition between the band and the localized pairs situation. The transition takes place forV/t= 1.4–0.1 and appears to be of essential singularity type. Comparison with other models used for pairing phenomena, like the negativeU-Hubbard model is made.     

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

The Klein-Gordon equation in D-dimensions for a recently proposed ring-shaped Kratzer potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the non-central equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three dimensions given by other works.      

Anharmonic Oscillator and Double-Well Potential: Approximating Eigenfunctions

A simple uniform approximation of the logarithmic derivative of the ground state eigenfunction for both the quantum-mechanical anharmonic oscillator and the double-well potential given by V=m ² x ²+g x ⁴ at arbitrary g ≥ 0 for m ²>0 and m ²<0, respectively, is presented. It is shown that if this approximation is taken as unperturbed problem it leads to an extremely fast convergent perturbation theory Mathematics Subject Classifications(2000) 34L40, 34B08, 41A99