Application of asymptotic iteration method to the Khare-Mandal and its PT-symmetric QES partner potential

We study the application of the asymptotic iteration method to the Khare-Mandal potential and its PT-symmetric partner. The eigenvalues and eigenfunctions for both potentials are obtained analytically. We have shown that although the quasi-exactly solvable energy eigenvalues of the Khare-Mandal potential are found to be in complex conjugate pairs for certain values of potential parameters, its PT-symmetric partner exhibits real energy eigenvalues in all cases.      

Bound state solutions of d-dimensional Schrödinger equation with Eckart potential plus modified deformed Hylleraas potential

We study the d-dimensional Schrödinger equation for Eckart plus modified deformed Hylleraas potentials using the generalized parametric form of Nikiforov-Uvarov method. We obtain energy eigenvalues and the corresponding wave function expressed in terms of Jacobi polynomial. We also discuss two special cases of this potential comprised of the Hulthen potential and the Rosen-Morse potential in three dimensions. Numerical results are also computed for the energy spectrum and the potentials.     

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

We investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ ₀, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ ₀ r ², we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ ₀, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.     

Exact pseudospin symmetry solution of the Dirac equation for spatially-dependent mass Coulomb potential including a Coulomb-like tensor interaction via asymptotic iteration method

In this Letter, the Dirac equation is exactly solved for spatially-dependent mass Coulomb potential including a Coulomb-like tensor potential under pseudospin symmetry limit by using asymptotic iteration method with arbitrary spin-orbit coupling number κ. The energy eigenvalues and corresponding eigenfunctions are obtained and some numerical results are given.     

Approximate solutions of Schrdinger equation for Eckart potential with centrifugal term

The approximate analytical solutions of the Schrdinger equation for the Eckart potential are presented for the arbitrary angular momentum by using a new approximation of the centrifugal term. The energy eigenvalues and the corresponding wavefunctions are obtained for different values of screening parameter. The numerical examples are presented and the results are in good agreement with the values in the literature. Three special cases, i.e., s-wave, ξ = λ = 1, and β = 0, are investigated.     

Bound states resulting from interaction of the non-relativistic particles with the multiparameter potential

In this study, we present the analytical solutions of bound states for the Schrodinger equation with the multiparameter potential containing the different types of physical potentials via the asymptotic iteration method by applying the Pekeristype approximation to the centrifugal potential. For any n and l(states) quantum numbers, we derive the relation that gives the energy eigenvalues for the bound states numerically and the corresponding normalized eigenfunctions. We also plot some graphics in order to investigate effects of the multiparameter potential parameters on the energy eigenvalues.Furthermore, we compare our results with the ones obtained in previous works and it is seen that our numerical results are in good agreement with the literature.     

A new Morse ring-shaped potential for diatomic molecules

Using the Pekeris approximation, the Schrödinger equation is solved analytically for the Morse plus a novel angle-dependent potential. The generalized parametric Nikiforov–Uvarov method is used to obtain energy eigenvalues and corresponding eigenfunctions. We present the effect of the angle-dependent part on radial solutions, and some numerical results for diatomic molecules are also given.     

Equation of state and interaction potential of helium under high temperatures and high densities

Based on the thermodynamics statistic method, the improved variational perturbation theory and the modified quantum mechanics correction model have been used to calculate the equation of state of liquid helium at pressure from 0.7 to 108 GPa. The calculation results are in good agreement with the experimental data. The EXP-6 potential (α = 13.1) can more accurately describe the interaction of helium atoms than other potentials in the scheme. Finally, a comparison is shown between our interatomic potentials and other potentials.     

Algebraic expressions for effective potential characteristic parameters in heavy ion scattering

In this paper, we obtain reliable expressions to calculate the barrier and pocket positions of the real part of the effective phenomenological optical potential having Woods-Saxon form factor, for different partial waves. The comparison of the results obtained from these formulae, when compared with the numerical results obtained using Newton-Raphson iterative procedure are found to be quite accurate, with error less than 1%. We also obtain algebraic expressions for estimatingl _poc, the angular momentum at which the potential pocket vanishes, the accuracy of which is tested with the exact calculations, using self-consistent iterative procedures. These and other expressions deduced in this paper provide simple and useful methods for calculating critical parameters of heavy ion effective potentials like barrier and pocket positions, curvatures at the barrier and pocket positions,l _poc and the grazing angular momentuml _g to carry out the analysis of heavy ion scattering.     

The energy eigenvalues of the Kratzer potential in the presence of a magnetic field

Two dimensional solution of the Schr?dinger equation for the Kratzer potential with and without the presence of a constant magnetic field is investigated within the framework of the asymptotic iteration method. The energy eigenvalues are analytically obtained for the absence of the magnetic field case. However, in the presence of a constant magnetic field, the energy eigenvalues are calculated numerically using the same method. The results obtained by using different Larmor frequencies and potential parameters are compared with the results of the absence of the magnetic field case (ω _L = 0). Effect of the magnetic field on the energy eigenvalues of the Kratzer potential is precisely presented.     

Spin symmetric solutions of Dirac equation with Pöschlben Teller potential

The approximate analytical solutions of the Dirac equation with the Pöschl—Teller potential is presented for arbitrary spin-orbit quantum number kappa within the framework of the spin symmetry concept. The energy eigenvalues and the corresponding two Dirac spinors are obtained approximately in closed forms. The limiting cases of the energy eigenvalues and the two Dirac spinors are briefly discussed.     

Rotation and vibration of diatomic molecule oscillator with hyperbolic potential function

The explicit expressions of energy eigenvalues and eigenfunctions of bound states for a three-dimensional diatomic molecule oscillator with a hyperbolic potential function are obtained approximately by means of the hypergeometric series method. Then for a one-dimensional system, the rigorous solutions of bound states are solved with a similar method. The eigenfunctions of a one-dimensional diatomic molecule oscillator, expressed in terms of the Jacobi polynomial, are employed as an orthonormal basis set, and the analytic expressions of matrix elements for position and momentum operators are given in a closed form.     

势问题的无单元Galerkin方法的误差估计

在高维情况下,首先研究了无单元Galerkin方法的形函数构造方法——移动最小二乘法在Sobolev空间W^k,p(Ω)中的误差估计.然后,在势问题的无单元Galerkin方法的基础上,研究了势问题的通过罚函数法施加本质边界条件的无单元Galerkin方法在Sobolev空间中的误差估计.当节点和形函数满足一定条件时,证明了该误差估计是最优阶的.从误差分析中可以看出,数值解的误差与权函数的影响半径密切相关.最后,通过算例验证了结论的正确性. 关键词： 无网格方法 无单元Galerkin方法 势问题 误差估计     

Pion-nucleus optical potential: The pion-absorption contribution

The real and imaginary parts of pion-nucleus optical potential arising from pion absorption channel have been computed. A two-nucleon model of pion absorption which includesπ andρ rescattering andS-wave interaction has been used. The effects of short-range nucleon-nucleon correlations, Pauli blocking and formfactors have been included. The threshold values of imaginary absorption potential are reasonably close to density-squared terms of phenomenological potentials. The real part ofP-wave potential is attractive and that ofS-wave potential is weakly attractive at lower pion energies and changes sign as pion energy is increased. The calculation shows that the real part of absorption is significantly affected by short-range correlations and Pauli-blocking.     

用代数-能量自洽法研究双原子分子解析势能函数

基于计算双原子分子完全振动能谱及离解能的代数方法 (algebraic method,AM)和研究双原子分子解析势能函数的能量自洽法(energy consistent method,ECM),建立了计算双核分子体系精确解析势能函数的代数-能量自洽法(AM-ECM).应用AM-ECM方法研究了7Li+2-23Σg,KH-X1Σ+,NaLi-X1Σ+和NaLi-A1Σ+电子态的解析势能表达形式,并与其他方法的研究结果进行了比较,获得了能正确描述这些电子态在渐近区和离解区的精确解析表达结果.     

Application of the quantum mechanical hypervirial theorems to even-power series potentials

The class of the even-power series potentials,V(r)=-D+∑ _k-0 ^∞ V_kλ^kr^2k+2,V ₀=ω²>0is studied with the aim of obtaining approximate analytic expressions for the nonrelativistic energy eigenvalues, the expectation values for the potential and kinetic energy operators, and the mean square radii of the orbits of a particle in its ground and excited states. We use the hypervirial theorems (HVT) in conjunction with the Hellmann-Feynman theorem (HFT), which provide a very powerful scheme for the treatment of the above and other types of potentials, as previous studies have shown. The formalism is reviewed and the expressions of the above-mentioned quantities are subsequently given in a convenient way in terms of the potential parameters, the mass of the particle, and the corresponding quantum numbers, and are then applied to the case of the Gaussian potential and to the potentialV(r)=−D/cosh²(r/R). These expressions are given in the form of series expansions, the first terms of which yield, in quite a number of cases, values of very satisfactory accuracy.     

Bound states of the Schrdinger equation for the Pschl-Teller double-ring-shaped Coulomb potential

Põschl--Teller double-ring-shaped Coulomb (PTDRSC) potential, the Coulomb potential surrounded by Põschl--Teller and double-ring-shaped inversed square potential, is put forward. In spherical polar coordinates, PTDRSC potential has supersymmetry and shape invariance in φ, θ and r coordinates. By using the method of supersymmetry and shape invariance, exact bound state solutions of Schrõdinger equation with PTDRSC potential are presented. The normalized φ, θ angular wave function expressed in terms of Jacobi polynomials and the normalized radial wave function expressed in terms of Laguerre polynomials are presented. Energy spectrum equations are obtained. Wave function and energy spectrum equations of the system are related to three quantum numbers and parameters of PTDRSC potential. The solutions of wave functions and corresponding eigenvalues are only suitable for the PTDRSC potential.     

The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

The generalized pseudospectral (GPS) method is employed to calculate the bound states of the Hulthén and the Yukawa potentials in quantum mechanics, with special emphasis onhigher excited states andstronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a non-uniform and optimal spatial discretization of the radial Schrödinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials withn <- 10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high asn = 17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. Then > 6 states of the Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulthén potential are reported here for the first time. Excepting the 1s and 2s states of the Yukawa potential, the present method surpasses the accuracy of all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials.     

The contribution of nuclear inelastic excitation to the optical potential for heavy ions

Using the plane-wave approximation we derive analytical expressions for both the real and imaginary parts of the polarization potential arising from nuclear inelastic scattering. These potentials and the resulting elastic and inelastic cross sections are compared with exact coupledchannel calculations for ¹³C on ⁴⁰Ca at 68 MeV. The agreement, for the most part, is good. We also briefly discuss the numerical non-local potentials for this system and the imaginary polarization potential for ¹⁶O on ²⁰⁸Pb at 104 MeV.     

不同势下铱团簇结构和熔化行为的分子动力学模拟

采用分子动力学方法及淬火技术,结合Gupta势和Sutton-Chen势,模拟研究了包含13,14,55,56,147及148个原子数的铱团簇的熔化行为. 结果表明,Gupta势和Sutton-Chen势对所研究的Ir团簇的基态几何结构和熔化行为给出了基本一致的描述：两种不同势给出了完全相同的基态几何结构;两种势给出的Ir团簇熔点及预熔化区间随团簇尺寸的变化关系基本一致;对于小Ir_n团簇（n=13,14）两类势均表现出比热峰值相对于均方根键长涨落饱和值滞后的现象. 但是 关键词： 铱团簇 分子动力学 Gupta势和Sutton-Chen势 熔化