两个严格可解的双原子分子势函数

提出了一个新的势函数，其Ｓｃｈｒ?ｄｉｎｇｅｒ方程严格可解．同时提出一个新的变量变换关系，严格求解了双曲型Ｐ?ｓｃｈｌ-Ｔｅｌｅｒ分子势Ｓｃｈｒ?ｄｉｎｇｅｒ方程的束缚态．得出的能级公式形式封闭、简单，归一化波函数用超几何级数表达．文献中关于Ｈｕｌｔｈéｎ势和修正Ｐ?ｓｃｈｌ-Ｔｅｌｅｒ势及无反射势的结果都作为特例包含在本文更一般的结论之中．最后，还讨论了本文势函数对双原子分子的实际应用． 关键词：     

修正Pschl-Teller势的薛定谔方程束缚态的一种解法

用一个新的变换求解了修正Ｐｓｃｈｌ－Ｔｅｌｅｒ势的薛定谔方程束缚态,得到了能量本征值及相应的波函数．     

量子系统的能量本征值在超对称性、形状不变性框架下的计算

在超对称性、形状不变性框架下，计算了一维修正Ｐｓｃｈｌ-Ｔｅｌｅｒ势、Ｎ维氢原子和Ｎ维各向同性谐振子的能量本征值．得到的能谱公式与用通常的因子化方法得到的严格解完全一致 关键词：     

修正Poschl—Teller势的Schrodinger方程束缚态的精确解

将修正Ｐｏｓｃｈｌ－Ｔｅｌｌｅｒ势的Ｓｃｈｒｏｄｉｎｇｅｒ方程作自变量双曲函数变换，使其转化为普遍的ａｓｓｏｃｉａｔｅｄ－Ｌｅｇｅｎｄｒｅ方程，用级数法解此方程，得到用普遍的ａｓｓｏｃｉａｔｅｄ－Ｌｅｇｅｎｄｒｅ多项式表示的修正Ｐｏｓｃｈｌ－Ｔｅｌｌｅｒ势的束缚态的归一化波函数，文献［１－５］中的有关结果都作为特例包含在本文的一般结论之中。     

修正Poechl—Teller势的薛定谔方程束缚态的一种解法

用一个新的变换求解了修正Ｐｏｅｓｃｈｌ－Ｔｅｌｌｅｒ势的薛定谔方程束缚态,得到了能量本征值及相应的波函数。     

严格可解四参数双原子分子势函数

提出一个四参数双原子分子势函数,对s波Schrdinger方程进行了严格求解,并采用一个简便的方法考虑了转动修正.该势函数对实验Rydberg-Klein-Rees曲线及振动-转动能级的计算精度远优于常用的Morse势,且将Morse势等势函数作为特例包括于其中. 关键词：     

一类广义N维非线性Schrdinger方程的孤子解及其性质研究

研究一类Ｎ维广义非线性Ｓｃｈｒｄｉｎｇｅｒ方程的孤子解及其性质，研究非线性参数α变化（α→０及α→∞）时孤子性态的变化规律，同时研究该问题的数值解法，得到了该方程的ＰＲ差分格式的收敛性和稳定性条件．     

量子系统的能量本征值在超对称性,形状不变性框架下的计算

在超对称性、形产太不变性框架下，计算了一维修正Ｐｏｓｃｈｌ－Ｔｅｌｌｅｒ势、Ｎ维氢原子和Ｎ维各向同性谱振子的能量本征值，得到的能谱公式与用通常的因子化方法得到的严格解完全一致。     

波函数的连续性和有界性与Schrdinger方程

本文从波函数ψ满足Ｓｃｈｒｄｉｎｇｅｒ方程出发，对波函数须满足的基本条件（即ψ必须连续、有界及单值）进行剖析，指出只要给定的势函数Ｖ有界，则ψ及ψ′都自然连续；若Ｖ没有二阶极点，则ψ有界     

无反射势的Schrdinger方程严格解的三维推广

文献[1]给出无反射势V(x)=-N(N+1)sech~2x当N为任意正整数时schrodinger方程束缚态和散射态的严格解。本文推广文献[1]的工作,继续给出三维情况下无反射势Schrodinger方程束缚态和散射态的严格解,并得到了与一维情况不同的一些物理结果。     

Prepotential approach to quasinormal modes

In this paper we demonstrate how the recently reported exactly and quasi-exactly solvable models admitting quasinormal modes can be constructed and classified very simply and directly by the newly proposed prepotential approach. These new models were previously obtained within the Lie-algebraic approach. Unlike the Lie-algebraic approach, the prepotential approach does not require any knowledge of the underlying symmetry of the system. It treats both quasi-exact and exact solvabilities on the same footing, and gives the potential as well as the eigenfunctions and eigenvalues simultaneously. We also present three new models with quasinormal modes: a new exactly solvable Morse-like model, and two new quasi-exactly solvable models of the Scarf II and generalized Pöschl–Teller types.     

Liouville Transformation and Exactly Solvable Schrodinger Equations

The present paper discusses the connectionbetween exactly solvable Schrodinger equations and theLiouville transformation. This transformation yields alarge class of exactly solvable potentials, including the exactly solvable potentials introduced byNatanzon. In addition, this class is shown to containtwo new families of exactly solvablepotentials.     

Supersymmetry in quantum mechanics

In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable. In this lecture I review the theoretical formulation of supersymmetric quantum mechanics and discuss many of its applications. I show that the well-known exactly solvable potentials can be understood in terms of a few basic ideas which include supersymmetric partner potentials and shape invariance. The connection between inverse scattering, isospectral potentials and supersymmetric quantum mechanics is discussed and multi-soliton solutions of the KdV equation are constructed. Further, it is pointed out that the connection between the solutions of the Dirac equation and the Schrödinger equation is exactly same as between the solutions of the MKdV and the KdV equations.     

On the definition of the resonance with examples two-channel models

In an exactly solvable model of separable potentials a two channel scattering problem is solved in l = 0 state. The location and the width of a resonance are then defined in three different ways and the resonance parameters so extracted are then compared. This problem is of interest vis-a-vis the Δ(3, 3) resonance parameters.     

Scattering amplitudes for multi-indexed extensions of solvable potentials

New solvable one-dimensional quantum mechanical scattering problems are presented. They are obtained from known solvable potentials by multiple Darboux transformations in terms of virtual and pseudo virtual wavefunctions. The same method applied to confining potentials, e.g.  Pöschl–Teller and the radial oscillator potentials, has generated the multi-indexed Jacobi and Laguerre polynomials. Simple multi-indexed formulas are derived for the transmission and reflection amplitudes of several solvable potentials.     

Complex oscillator and Painlevé IV equation

Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. In this article the first- and second-order supersymmetric transformations will be used to obtain new exactly solvable potentials departing from the complex oscillator. The corresponding Hamiltonians turn out to be ruled by polynomial Heisenberg algebras. By applying a mechanism to reduce to second the order of these algebras, the connection with the Painlevé IV equation is achieved, thus giving place to new solutions for the Painlevé IV equation.     

He-O_2转动激发截面的理论计算

用公认精确的密耦 (Close Coupling)方法、采用两种不同的相互作用势计算了He -O2 碰撞的态 态转动激发截面 (E =2 6.8meV) ,通过系统研究和计算发现 :低能散射时 ,He -O2 碰撞的弹性散射主要发生在小角部分 ,而非弹性转动激发主要发生在大角部分。研究表明 :转动激发截面对势能表面的方向性和散射角都非常敏感。     

Exactly solvable two-dimensional stationary Schrödinger operators obtained by the nonlocal Darboux transformation

The Fokker–Planck equation associated with the two-dimensional stationary Schrödinger equation has the conservation law form that yields a pair of potential equations. The special form of Darboux transformation of the potential equations system is considered. As the potential variable is a nonlocal variable for the Schrödinger equation that provides the nonlocal Darboux transformation for the Schrödinger equation. This nonlocal transformation is applied for obtaining of the exactly solvable two-dimensional stationary Schrödinger equations. The examples of exactly solvable two-dimensional stationary Schrödinger operators with smooth potentials decaying at infinity are obtained.     

Relativistic Confinement of Neutral Fermions with Partially Exactly Solvable and Exactly Solvable PT-Symmetric Potentials in the Presence of Position-Dependent Mass

The relativistic problems of neutral fermions subject to a new partially exactly solvable PT-symmetric potential and an exactly solvable PT-symmetric hyperbolic cosecant potential in 1+1 dimensions are investigated. The Dirac equation with the double-well-like mass distribution in the background of the PT-symmetric vector potential coupling can be mapped into the Schrödinger-like equation with the partially exactly solvable double-well potential. The position-dependent effective mass Dirac equation with the PT-symmetric hyperbolic cosecant potential can be mapped into the Schrödinger-like equation with the exactly solvable modified Pöschl-Teller potential. The real relativistic energy levels and corresponding spinor wavefunctions for the bound states have been given in a closed form.