Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry

In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning-Rosen potential for arbitrary spin-orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin-orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin-orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning-Rosen potential.     

Solutions to the Modified Pöschl-Teller Potential in D-Dimensions

An approximate solution of the D-dimensional Schrödinger equation with the modified Pöschl-Teller potential is obtained with an approximation of the centrifugal term. Solution to the corresponding hyper-radial equation is given using the conventional Nikiforov-Uvarov method. The normalization constants for the Pöschl-Teller potential are also computed. The expectation values of -2_> and are also obtained using the Feynman-Hellmann theorem.     

Energy spectrum of the trigonometric Rosen-Morse potential using an improved quantization rule

The improved quantization rule simplifies the calculation of the energy levels for the exactly solvable quantum system. In this Letter we calculate the energy levels of the Schrödinger equation with the symmetric and asymmetric trigonometric Rosen-Morse potentials by the improved quantization rule.     

Arbitrary l-state solutions of the rotating Morse potential through the exact quantization rule method

By using the exact quantization rule, for non-zero l   values we present analytical solutions of the radial Schrödinger equation for the rotating Morse potential in the frame of the Pekeris approximation. The energy levels of all the bound states are easily calculated from this quantization rule. Especially, the intractable normalized wavefunctions are also obtained. The numerical calculations for three typical diatomic molecules HCl, CO and LiH are compared with those obtained by other methods such as the supersymmetry, the Fourier gird Hamiltonian, the asymptotic iteration, the variational, the Nikiforov–Uvarov, the shifted 1/N$1/N$ expansion and the modified shifted 1/N$1/N$ expansion. It is found that the results obtained by the present method are in good agreement with those obtained by other approximate methods.     

Classical motion and coherent states for Pöschl-Teller potentials

The trigonometric and hyperbolic Pöschl-Teller potentials are dealt with from the point of view of classical and quantum mechanics. We show that there is a natural correspondence between the algebraic structure of these two approaches for both kind of potentials. Then, the coherent states are constructed and the appropriate classical variables are compared with the expected values of their corresponding quantum operators.     

Exact Solutions of Klein--Gordon Equation with Scalar and Vector Rosen--Morse-Type Potentials

We obtain an exact analytical solution of the Klein Gordon equation for the equal vector and scalar Rosen Morse and Eckart potentials as well as the parity-time （PT） symmetric version of the these potentials by using the asymptotic iteration method. Although these PT symmetric potentials are non-Hermitian, the corresponding eigenvalues are real as a result of the PT symmetry.     

Singular short range potentials in the J-matrix approach

We use the tools of the J-matrix method to evaluate the S-matrix and then deduce the bound and resonance states energies for singular screened Coulomb potentials, both analytic and piecewise differentiable. The J-matrix approach allows us to absorb the 1/r singularity of the potential in the reference Hamiltonian, which is then handled analytically. The calculation is performed using an infinite square integrable basis that supports a tridiagonal matrix representation for the reference Hamiltonian. The remaining part of the potential, which is bound and regular everywhere, is treated by an efficient numerical scheme in a suitable basis using Gauss quadrature approximation. To exhibit the power of our approach we have considered the most delicate region close to the bound-unbound transition and compared our results favorably with available numerical data.     

Generalized Morse and Pöschl-Teller potentials: The connection via Schrödinger equation

A systematic and unified treatment to connect the Schrödinger equation for generalized Morse and Pöschl-Teller potentials, generated by supersymmetry quantum mechanics, is used. An algebraic treatment of bound-state problems is presented.     

Exact solution of the Dirac equation with the Mie-type potential under the pseudospin and spin symmetry limit

We investigate the exact solution of the Dirac equation for the Mie-type potentials under the conditions of pseudospin and spin symmetry limits. The bound state energy equations and the corresponding two-component spinor wave functions of the Dirac particles for the Mie-type potentials with pseudospin and spin symmetry are obtained. We use the asymptotic iteration method in the calculations. Closed forms of the energy eigenvalues are obtained for any spin-orbit coupling term κ. We also investigate the energy eigenvalues of the Dirac particles for the well-known Kratzer-Fues and modified Kratzer potentials which are Mie-type potentials.     

Any l-state solutions of the Klein-Gordon equation with the generalized Hulthén potential

We present analytical solutions of the Klein-Gordon equation with non-zero l values for the general Hulthén potential within the framework of an approximation to the centrifugal potential for any l-states. The explicit expressions of bound state energy eigenvalues and eigenfunctions are derived. Three special cases, s-wave, standard Hulthén potential and ground state are discussed.     

Exact scattering length for a potential of Lennard-Jones type

For a modified Lennard-Jones interaction potential of the form ∼[(r₀/r)^2n-2-(r₀/r)ⁿ], an exact and simple expression for the s-wave scattering length is presented, and discussed in some detail. For heavy alkali atoms, which nowadays are routinely being employed to produce Bose-Einstein condensates, this potential is well compatible with known experimental data when n = 6.     

Convergent iterative solutions of Schroedinger equation for a generalized double well potential

We present an explicit convergent iterative solution for the lowest energy state of the Schroedinger equation with a generalized double well potential . The condition for the convergence of the iteration procedure and the dependence of the shape of the groundstate wave function on the parameter a are discussed.     

用点正则变换方法求解双原子分子的双曲型P?schl-Teller势的束缚态

采用在点正则变换下形状不变势的映射方法,给出了将Poschl-Teller Ⅰ势映射至Poschl-Teller Ⅱ势的点正则变换,并从Poschl-TellerI势的束缚态能级和波函数求得了Poschl-Teller Ⅱ势的束缚态能级和波函数.     

Solutions of Dirac equations with the Pöschl-Teller potential

By using the basic concepts of the supersymmetric quantum mechanics formalism and the function analysis method, we solve the Dirac equation with vector and scalar potentials and obtain the bound-state solutions for the nuclei in the relativistic P?schl-Teller potential. All of the analyses are prepared under the conditions of the exact spin symmetry and pseudospin symmetry. The exact energy equation and corresponding two-component spinor wave functions for s -wave bound states are obtained analytically.     

Accurate delta potential approximation for a coordinate-dependent potential and its analytical solution

In this Letter, analytical expression in recursive form for reflection amplitude is derived through a transformation which reduces the equation of motion for a coordinate-dependent potential to an equation with a chain of delta function potentials. The formulation provides accurate results of eigenvalues of bound and resonance states generated by a variety of potentials.     

Comment on: “Any l-state solutions of the Klein-Gordon equation with the generalized Hulthén potential”

It is shown that the bound l-state solutions of the Klein-Gordon equation for the general scalar and vector Hulthén potentials obtained by Qiang et al. are valid only for q?1 and . We clarify the problem and give the correct solutions when 0<q<1 or q<0. In each case, we derive a transcendental quantization condition for the s-state energy levels.     

Dynamical algebras for Pöschl-Teller Hamiltonian hierarchies

The dynamical algebras of the trigonometric and hyperbolic symmetric Pöschl-Teller Hamiltonian hierarchies are obtained. A kind of discrete-differential realizations of these algebras are found which are isomorphic to so(3, 2) Lie algebras. In order to get them, first the relation between ladder and factor operators is investigated. In particular, the action of the ladder operators on normalized eigenfunctions is found explicitly. Then, the whole dynamical algebras are generated in a straightforward way.     

Exact solutions for vibrational levels of the Morse potential via the asymptotic iteration method

Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that the numerical results for the energy eigenvalues of⁷Li₂ are all in excellent agreement with those obtained before. Without any loss of generality, other states and other diatomic molecules could be treated in a similar way.     

Controllability of pure states for the Pöschl-Teller potential with a dynamical group SU(2)

The controllability of a quantum system for the modified Pöschl-Teller (MPT) potential with the discrete bound states is investigated. The creation and annihilation operators of this potential are constructed directly from the normalized wave function with the factorization method and associated to an su(2) algebra. It is shown that this quantum system with the nondegenerate discrete bound states can, in principle, be strongly completely controllable, i.e., the system eigenstates can be guided by the external field to approach arbitrarily close to a target state, which could be theoretically realized by the actions of the creation and annihilation operators on the ground state.     

Closed expressions for matrix elements of the trigonometric Pöschl-Teller potential

Analytical matrix elements of the xn (n>0) and m[tan(x)]m^′[cos(x)]dn/dxn operators are derived using the eigenfunctions of the symmetric trigonometric Pöschl-Teller potential. The closed formulas are written in terms of Gauss hypergeometric functions and could be used in variational calculations to describe vibrational energy levels associated with bending modes. Multiprecision computational packages are considered in order to obtain an arbitrary level of precision.