Arbitrary $\ell$-state solutions of the Klein-Gordon equation with the Manning-Rosen plus a Class of Yukawa potentials

Ro-vibrational energy analysis of Manning-Rosen and Pöschl-Teller potentials with a new improved approximation in the centrifugal term

Two physically important potentials (Manning-Rosen and Pöschl-Teller) are considered for the ro-vibrational energy in diatomic molecules. An improved new approximation is invoked for the centrifugal term, which is then used for their solution within the Nikiforov-Uvarov framework. This employs a recently proposed scheme, which combines the two widely used Greene-Aldrich and Pekeris-type approximations. Thus, approximate analytical expressions are derived for eigenvalues and eigenfunctions. The energies are examined with respect to two approximation parameters, $λ$ and $ν$. The original approxi…

An improved approximation to l-wave bound states of the Manning-Rosen potential by Nikiforov-Uvarov method

A new approximation scheme to the centrifugal term is proposed to obtain the $l\neq 0$ solutions of the Schrödinger equation with the Manning-Rosen potential. We also find the corresponding normalized wave functions in terms of the Jacobi polynomials. To show the accuracy of the new approximation scheme, we calculate the energy eigenvalues numerically for arbitrary quantum numbers $n$ and $l$ with two different values of the potential parameter $α.$ The bound state energies of various states for a few $% HCl,$ $CH,$ $LiH$ and $CO$ diatomic molecules are also calculated. The numerical results a…

Manning Rosen 加指数 Yukawa 势的本征解与热力学性质

Eigen Solution and Thermodynamic Properties of Manning Rosen Plus Exponential Yukawa Potential

本文利用参数化 Nikiforov-Uvarov 方法求解 Manning Rosen 加指数 Yukawa 势的薛定谔方程，得到束缚态解、归一化波函数和能量本征方程，并计算了配分函数及多种振动热力学性质，数值结果与已有文献吻合良好。

Exact Solutions of the Klein-Gordon Equation for the Rosen-Morse type Potentials via Nikiforov-Uvarov Method

The exact solutions of the one-dimensional Klein-Gordon equation for the Rosen-Morse type potential with equal scalar and vector potentials are presented. First we briefly review Nikiforov-Uvarov mathematical method. Using this method, wave-functions and corresponding exact energy equation are obtained for the s-wave bound state. It has been shown that the results for Rosen-Morse type potentials reduce to standard Rosen-Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

Path integral solution for a Klein-Gordon particle in vector and scalar deformed radial Rosen-Morse-type potentials

The problem of a Klein-Gordon particle moving in equal vector and scalar Rosen-Morse-type potentials is solved in the framework of Feynman's path integral approach. Explicit path integration leads to a closed form for the radial Green's function associated with different shapes of the potentials. For $q\leq -1$, and $\frac{1}{2α}\ln \left\vert q\right\vert <r<+\infty $, the energy equation and the corresponding wave functions are deduced for the $l$ states using an appropriate approximation to the centrifugal potential term. When $-1<q<0$ or $q>0$, it is shown that the quantization conditions …

Approximate Analytical Solutions of a Two-Term Diatomic Molecular Potential with Centrifugal Barrier

Approximate analytical bound state solutions of the radial Schrödinger equation are studied for a two-term diatomic molecular potential in terms of the hypergeometric functions for the cases where $q\geq1$ and $q=0$. The energy eigenvalues and the corresponding normalized wave functions of the Manning-Rosen potential, the 'standard' Hulthén potential and the generalized Morse potential are briefly studied as special cases. It is observed that our analytical results are the same with the ones obtained before.

Relativistic Approximate Solutions for a Two-Term Potential: Riemann-Type Equation

Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be written in terms of hypergeometric function $\,_{2}F_{1}(a,b;c;z)$. The energy eigenvalue equations and the corresponding normalized wave functions are given both for two wave equations. The results for some special cases including the Manning-Rosen potential, the Hulthén potential and the Coulomb potential are also discussed by setting the parameters as re…

Antiparticle in Light of Einstein-Podolsky-Rosen Paradox and Klein Paradox

The original version of Einstein-Podolsky-Rosen (EPR) paradox and the Klein paradox of Klein-Gordon (KG) equation are discussed to show the necessity of existence of antiparticle with its wavefunction being fixed unambiguously. No concept of "hole" is needed.

Bound states of the Klein-Gordon equation in D-dimensions with some physical scalar and vector exponential-type potentials including orbital centrifugal term

The approximate analytic bound state solutions of the Klein-Gordon equation with equal scalar and vector exponential-type potentials including the centrifugal potential term are obtained for any arbitrary orbital angular momentum number l and dimensional space D. The relativistic/non-relativistic energy spectrum equation and the corresponding unnormalized radial wave functions, in terms of the Jacobi polynomials P_{n}^{(α,β)}(z), where α>-1, β>-1 and z\in[-1,+1] or the generalized hypergeometric functions _{2}F_{1}(a,b;c;z), are found. The Nikiforov-Uvarov (NU) method is used in the solution. …

Exact Quantized Momentum Eigenvalues and Eigenstates of a General Potential Model

We obtain the quantized momentum eigenvalues, $P_n$ , and the momentum eigenstates for the space-like Schrödinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter…

重新审视Rosen-Morse型势的薛定谔方程及其应用

The Schrödinger equation for the Rosen-Morse type potential revisited with applications

本文利用Nikiforov-Uvarov方法严格求解Rosen-Morse型势的定态薛定谔方程，得到包含束缚态和非束缚态的完整解，并据此证明$φ^{2p+2}$型势非线性Klein-Gordon方程扭结的稳定性，同时推导了本征函数的正交性与完备性关系。

Constraint polynomial approach -- an alternative to the functional Bethe Ansatz method?

Recently developed general constraint polynomial approach is shown to replace a set of algebraic equations of the functional Bethe Ansatz method by a single polynomial constraint. As the proof of principle, the usefulness of the method is demonstrated for a number of quasi-exactly solvable (QES) potentials of the Schrödinger equation, such as two different sets of modified Manning potentials with three parameters, an electron in Coulomb and magnetic fields and relative motion of two electrons in an external oscillator potential, the hyperbolic Razavy potential, and a (perturbed) double sinh-Go…

利用Nikiforov--Uvarov方法求解有效场修正径向薛定谔方程的精确解析谱

Exact analytical spectra of an effective field-modified radial Schrödinger equation by the Nikiforov--Uvarov method

本研究利用Nikiforov--Uvarov方法，精确求解了共线电磁场中无自旋带电粒子的有效径向薛定谔方程，给出三类势分量的闭式解及相关结果，验证了解析正确性。