对矩形域上第二边值求解问题的两种改进方法

本文首先讨论了对矩形域上第二边值问题求解的一般方法,即分离变量的方法,说明一些因素对求解的重要影响,从而进一步探讨了对矩形域上第二边值求解问题的两种改进方法。

Mathematica 8.0.1中文版在量子力学教学中的应用

首先介绍了Mathematica系统简单操作与功能,然后重点介绍了Mathematica 8.0.1中文版在量子力学教学中的应用,包括如何用久期方程求解本征值和本征波函数,如何根据薛定谔方程求解波函数态矢量的演化。通过举例可以清晰的看到利用Mathematica 8可以很容易的求解上述的量子力学问题。

用超几何级数方法解任意l态双曲正切势场

对于s态的双曲正切势场下的Schrdinger的径向方程,则能精确求出能量本征值和对应的波函数的表达式.对于非零的l态,则不能精确求解双曲势场下的在Schrdinger的径向方程.本文针对不能精确求解非零的l态,从另一方面出发,能利用近似的方法得到能量本征值和对应的本征函数的表达式.应用类似的Pekeris近似方法,将含有角动量的一项在r0处展开,省略高阶项,原双曲正切势场Schrdinger的径向方程变化成为超几何方程.应用超几何级数方法,得到了能量本征值和对应的本征函数的表达式.最后进行数值的验算,取两组不同的数值来计算能量本征值,得出结果基本一致,数值结果表明此法是可靠和有效的.

Approximate Bound State Solutions of DKP Equation for Any J State in the Presence of Woods-Saxon Potential

We study Duffin-Kemmer-Petiau(DKP) equation in the presence of the Woods-Saxon potential and obtain eigenvalues and corresponding eigenfunctions for any J state by using of the Nikiforov-Uvarov(NU) method.The Pekeris approximation is used to deal with centrifugal term.

Proof of a conjecture on a discretized elliptic equation with cubic nonlinearity

We sharpen and prove a conjecture suggested by Chen and Xie, which states that in Galerkineigenfunction discretization for -Δu = u3 , when the finite-dimensional subspace is taken as the eigensubspace corresponding to an N-fold eigenvalue of -Δ, the discretized problem has at least 3N-1 distinct nonzero solutions. We also present a related result on the multiplicities of eigenvalues of -Δ.

Approximate Bound States Solution of the Hellmann Potential

The Hellmann potential, which is a superposition of an attractive Coulomb potential -air and a Yutmwa potential b e-δr /r , is often used to compute bound-state normalizations and energy levels of neutral atoms. By using the generalized parametric Nikiforov-Uvarov （NU） method, we have obtained the approximate analytical solutions of the radial Schr6dinger equation （SE） for the Hellmann potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented, which show good agreement with a numerical amplitude phase method and also those previously obtained by other methods. As a particular case, we find the energy levels of the pure Coulomb potential.

Analytical Approximate Solution of Schr?dinger Equation in D Dimensions with Quadratic Exponential-Type Potential for Arbitrary l-State

We present the bound state solution of Schr6dinger equation in D dimensions for quadratic exponential-type potential for arbitrary l-state. We use generalized parametric Nikiforov-Uvarov method to obtain the energy levels and the corresponding eigenfunction in dosed form. We also compute the energy eigenvalues numerically.

Dirac Equation and Some Quasi-Exact Solvable Potentials in the Turbiner's Classification

In this paper quasi-exact solvability （QES） of Dirac equation with some scalar potentials based on s/（2） Lie algebra is studied. According to the quasi-exact solvability theory, we construct the configuration of the classes II, IV, V, and X potentials in the Turbiner＇s classification such that solved and the Bethe ansatz equations are derived in order to the Dirac equation with scalar potential is quasi-exactly obtain the energy eigenvalues and eigenfunctions.

Solution of Dirac Equation with Generalized Hylleraas Potential

We employ the parametric generalization of the Nikiforov-Uvarov method to solve the Alhaidari formal- ism of the Dirac equation with a generalized Hylleraas potential of the form V（τ）= V0（a ＋ exp （λτ））/（b ＋ exp （λτ）） ＋ V1（ d ＋ exp （ λτ） ） / （b ＋ exp （λτ））. We obtain the bound state energy eigenvalue and the corresponding eigenfunction ex- pressed in terms of the Jaeobi polynomials. By choosing appropriate parameter in the potential model, the generalized Hylleraas potential reduces to the well known potentials as special cases.

Solutions of Woods-Saxon Potential with Spin-Orbit and Centrifugal Terms through Nikiforov-Uvarov Method

In this study, the analytical solutions of the radial Schr6dinger equation for the central Woods-Saxon potential together with spin-orbit interaction and centrifugal terms have been derived by using Nikiforov-Uvarov method. The energy eigenvalues and corresponding eigenfunctions of nucleons have been obtained for various values of n, l, and j quantum numbers. The obtained results using this method are in satisfactory agreement with available data in the speciM case.

Prescribing Curvature Problems on the Bakry-Emery Ricci Tensor of a Compact Manifold with Boundary

t The authors consider the problem of conformally deforming a metric such that the k-curvature defined by an elementary symmetric function of the eigenvalues of the Bakry-Emery Ricci tensor on a compact manifold with boundary to a prescribed function. A consequence of our main result is that there exists a complete metric such that the Monge-Amp^re type equation with respect to its Bakry-Emery Ricci tensor is solvable, provided that the initial Bakry-Emery Ricci tensor belongs to a negative convex cone.

Investigation of Fermions in Non-commutative Space by Considering Kratzer Potential

The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.