任意维l态Woods-Saxon势的精确解

在D维空间下使用完全量子化规则计算了具有离心项的Woods-Saxon势,根据动量积分 (其中 )和Pekeris近似化条件,得到了系统的任意l波Schrödinger方程的解和能谱方程．讨论了束缚态能谱的有关性质．     

具有Manning-Rosen势的Schrödinger方程的任意l波束缚态解析解

使用完全量子化规则计算了具有离心项的Manning-Rosen势，根据动量积分 (其中 )和一种新的近似化条件，得到了系统的任意l波Schrödinger方程的解析解和能谱方程。最后简单讨论了l=0和α=0或1束缚态能谱的有关性质。     

双环形Hulthén势束缚态的近似解析解

构造了双环形Hulthén势, 用指数函数近似表示任意分波的离心项, 运用函数分析法讨论双环型Hulthén势Schrödinger方程的束缚态解. 归一化的角向波函数和径向波函数用超几何多项式表示, 给出了束缚态能谱, 体系的束缚态的能谱方程和波函数与量子数和势参数有关. 中心势场和单环形势场角向波函数及 Hulthén势束缚态能谱是本文双环形Hulthén势的特例. 关键词： 双环形Hulthén势 任意分波 近似解析解 束缚态     

环形振子势的精确解

将环形振子势的Schrödinger方程在球坐标系中进行变量分离.然后求解了角向方程和径向方程,给出了精确的能谱方程.获得了用普遍的缔合Legendre多项式表示的归一化的角向波函数和用合流超几何函数表示的归一化的径向波函数.     

HT-6M中性注入加热电荷交换能谱分析

用电荷交换中性粒子能谱分析的方法,研究了HT-6M托卡马克中性注入加热期间的氢离子能谱,得到了离子温度的增加。测量结果与实验定标律的估算在误差范围内相符;并与根据Fokker-Planck方程计算的注入过程中的离子能谱和温度变化进行了比较。 关键词：     

A=15和17原子核的单粒能潜与核力势

根据由格林函数方法导得的满壳层相邻核能谱所满足的方程,应用Hamada-Johnston势、Reid软心势和Paris势计算了¹⁵O和¹⁷O的单粒能谱,比较表明Paris势与实验符合最好。     

电荷不连续时电容耦合介观电路的量子回路方程及其能谱

考虑电荷具有不连续性的事实对双LC介观电路进行量子化,给出耦合形式的量子回路方程以及无相互作用Hamilton本征基矢下的电路能谱.结果表明,计及电荷离散性将使回路方程的形式发生明显变化;介观电路的能谱除与电路参数相关外,还明显地依赖于电荷的量子化性质.     

在赝自旋对称性势场中运动的相对论粒子的束缚态

在赝自旋对称性条件下,分别求解了在Kratzer型、Hulthén型和Poschl-Teller型标量势与矢量势场中运动的相对论粒子的Klein-Gordon方程和Dirac方程,给出了它们的束缚态能谱和相对论性波函数.     

库仑势加新环形势的相对论束缚态

在标量势等于矢量势的条件下，获得了库仑势加新环形势的Klein-Gordon方程和Dirac方程的束缚态的精确解. 对于Klein-Gordon方程，获得了精确的能谱方程和归一化的波函数. 对于Dirac方程，给出了精确的能谱方程和归一化的旋量波函数. 关键词： 库仑势加新环形势 束缚态 精确解     

相对论性无自旋粒子在Hartmann势场中运动的精确解

在标量势等于矢量势的条件下,本文获得了具有Hartmann型势的Klein-Gordon方程的精确解.给出了束缚态的精确的能谱方程和归一化的径向波函数,对于散射态,获得了按“k/2π标度”归一化的径向波函数和相移的解析计算公式.讨论了散射振幅的解析性质和波函数、能谱方程以及相移的非相对论近似.     

Vertex constants (asymptotic normalization coefficients) and mean-square radii of hypernuclei in the potential model

The vertex constants, asymptotic normalization coefficients, and mean-square radii for a number of Λ hypernuclei have been calculated in a wide range of mass numbers. Interaction of a Λ hyperon with a core nucleus was described by the Woods-Saxon, Hultén, and Yukawa potentials. Geometric parameters of the Woods-Saxon potential were taken from the data in the literature, and the interaction force was fitted to the experimental binding energy of the ground state of this hypernucleus. The parameters of the Hulthén and Yukawa potentials were chosen so as to reproduce simultaneously the binding energy of the hyperon and its mean-square radius calculated with the Woods-Saxon potential. Within the effective-radius approximation, the low-energy parameters for hyperon scattering by the core nucleus are expressed in terms of vertex constants and the numerical values of these parameters are determined.     

精确的量子化条件和不变量

提出并证明了一维量子系统和三维球对称量子系统的一个精确的量子化条件.在此精确量子化条件中, 除了通常的Nπ项外, 还有一积分项, 称为修正项. 发现该修正项正是在超对称量子力学中所谓的有形状不变势的量子系统的一个不变量，它不依赖于波函数的节点数.对这些系统, 可用基态能级和波函数确定此不变量的值, 从而由精确的量子化条件容易算出全部束缚态的能级. 计算得到能级的正确性又反过来验证了在有形状不变势的量子系统中此修正项确实是不变量.计算的有形状不变势的量子系统, 包括一维的有限方势阱、Morse势及其变形、R 关键词： 量子化条件 超对称量子力学 形状不变势 不变量     

Proper quantization rule as a good candidate to semiclassical quantization rules

In this article, we present proper quantization rule, ∫k(x) dx ‐ ∫k₀(x) dx = nπ, where and study solvable potentials. We find that the energy spectra of solvable systems can be calculated only from its ground state obtained by the Sturm‐Liouville theorem. The previous complicated and tedious integral calculations involved in exact quantization rule are greatly simplified. The beauty and simplicity of proper quantization rule come from its meaning – whenever the number of the nodes of the logarithmic derivative ?(x) = ψ(x)^‐1dψ(x) /dx or the number of the nodes of the wave function ψ(x) increases by one, the momentum integral will increase by π. We apply two different quantization rules to carry out a few typically solvable quantum systems such as the one‐dimensional harmonic oscillator, the Morse potential and its generalization as well as the asymmetrical trigonometric Scarf potential and show a great advantage of the proper quantization rule over the original exact quantization rule.     

Energy spectra of the hyperbolic and second Pöschl-Teller like potentials solved by new exact quantization rule

A new exact quantization rule simplifies the calculation of the energy levels for the exactly solvable quantum system. In this work we calculate the energy levels of the Schrödinger equation with the hyperbolic potential by this quantization rule. The corresponding eigenfunction is also derived for completeness. The second Pöschl-Teller like potential case is also carried out.     

Entrance Channel Mass Asymmetry Effects in Sub-Barrier Fusion Dynamics by Using Energy Dependent Woods-Saxon Potential

The present article highlights the inconsistency of static Woods-Saxon potential and the applicability of energy dependentWoods-Saxon potential to explore the fusion dynamics of ₂₂⁴⁸Ti+₂₈^58,60,64Ni, ₂₂⁴⁶Ti+₂₈⁶⁴Ni, ₂₂⁵⁰Ti+₂₈⁶⁰Ni, and ₉¹⁹F+₄₁⁹³Nb reactions leading to formation of different Sn-isotopes via different entrance channels. Theoretical calculations based upon one-dimensional Wong formula obtained by using static Woods-Saxon potential unable to provide proper explanation for sub-barrier fusion enhancement of these projectile-target combinations. However, the predictions of one- dimensional Wong formula based upon energy dependent Woods-Saxon potential model (EDWSP model) accurately describe the observed fusion dynamics of these systems wherein the significantly larger value of diffuseness parameter ranging from a = 0.85 fm to a = 0.97 fm is required to address the experimental data in whole range of energy. Therefore, the energy dependence in nucleus-nucleus potential simulates the influence of the nuclear structure degrees of freedom of the colliding pairs.     

Energy Spectrum of the Relativistic Duffin-Kemmer-Petiau Equation

The bound state energy eigenvalues for the relativistic DKP oscillator and DKP Coulomb potentials are determined by using an exact quantization rule. The corresponding eigenfunctions are also obtained. The results are consistent with those obtained by others methods.     

Solving the two-center nuclear shell-model problem with arbitrarily oriented deformed potentials

A general new technique to solve the two-center problem with arbitrarily oriented deformed realistic potentials is demonstrated, which is based on the powerful potential separable expansion method. As an example, molecular single-particle spectra for (12)C+(12)C-->(24)Mg are calculated using deformed Woods-Saxon potentials. These clearly show that nonaxial symmetric configurations play a crucial role in molecular resonances observed in reaction processes for this system at low energy.     

Energy for Two-electron Quantum Dots: The Quantization Rule Approach

The energy spectra for two electrons in a parabolic quantum dot are calculated by the quantization rule approach. The numerical results are in excellent agreement with the results by the method of integrating directly the Schr?dinger equation, and better than those by the WKB method and the WKB-DP method.     

A rotational model description of F

Rotational-particle coupling (RPC) model calculations have been performed for the positive parity states of ¹⁹F using a deformed oscillator potential (Nilsson) and a deformed Woods-Saxon potential. The energy spectra and spectroscopic factors (for the ¹⁸O(³He, d)¹⁹F reaction) are very similar for both calculations and in good agreement with experimental values and with recent full intermediate coupling shell-model calculations.