Arbitrary L-state Research Articles

Eigensolutions and thermodynamic properties of deformed and modified Morse potential model

A four parameter exponential-type potential known as the deformed and modified Morse potential model was proposed. The solution of the one-dimensional radial Schrӧdinger equation was obtained in the presence of the proposed potential for an arbitrary ℓ-state using a parametric Nikiforov–Uvarov method. The energy equation was used to obtain the eigenvalues for the cesium molecule and tin carbide for various states. The effects of the deformed parameter on the eigenvalues were studied. The result for the Morse potential was obtained by fixing the deformed parameter to zero. Finally, the thermal properties of the proposed potential and the Morse potential were studied in detail. The result obtained revealed that the behavior of the energy eigenvalue for the deformed and modified Morse potential with the deformed parameter (b) equals one, is same as the behavior of the energy eigenvalue for the actual Morse potential.

New bound-state solutions of the deformed Klein–gordon and Schrödinger equations for arbitrary l-state with the modified equal vector and scalar Manning–Rosen plus a class of Yukawa potentials in RNCQM and NRNCQM symmetries

New bound-state solutions of the deformed Klein–gordon and Schrödinger equations for arbitrary l-state with the modified equal vector and scalar Manning–Rosen plus a class of Yukawa potentials in RNCQM and NRNCQM symmetries

Bound-state solutions of the modified Klein–Gordon and Schrödinger equations for arbitrary l-state with the modified Morse potential in the symmetries of noncommutative quantum mechanics

Bound-state solutions of the modified Klein–Gordon and Schrödinger equations for arbitrary l-state with the modified Morse potential in the symmetries of noncommutative quantum mechanics

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

Focusing on an improved approximation scheme, we present how to treat the centrifugal and the Coulombic behavior terms and then to obtain the bound state solutions of the Klein-Gordon (KG) equation with the Manning-Rosen plus a Class of Yukawa potentials. By means of the Nikiforov-Uvarov (NU) and supersymmetric quantum mechanics (SUSYQM) methods, we present the energy spectrum for any ℓ-state and the corresponding radial wave functions in terms of the hypergeometric functions. From both methods we obtain the same results. Several special cases for the potentials which are useful for other physical systems are also discussed. These are consistent with those results in previous works. We obtain that the energy level E is sensitive to the potential parameter δ at fixed values of other parameters and increases when δ runs from 0.05 to 0.3. Furthermore, E is sensitive to the quantum numbers ℓ and nr for a given δ, as expected.

The Arbitrary l-state Solutions of the Hellmann Potential by Feynman Path Integral Approach

In this study, we used the Path integral method to obtain the bound state solutions of the Hellmann potential. Firstly we analytically derived the radial kernel expression of the Hellmann potential using the approximation of the centrifugal term and space-time transformations. Then we calculated the exact energy spectrum and the normalized eigenfunction from the poles of the Green function and their residues. We expressed normalized wave functions in terms of Jacobi polynoms and Hypergeometric functions.

The D-dimensional non-relativistic particle in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials

The D-Dimensional Non-Relativistic Particle Properties in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials was investigated using an analytical method. The bound state energy is given approximately in the closed form. The approximate wave function for arbitrary l-state in D-dimensions are expressed in the form of generalised Jacobi Polynomials. The energy spectra of the particle are increased when the dimensions are higher. The relationship between the orbital number in each dimension is recursive. The special case in 3 dimensions is given to the ground state.

Arbitrary l-state Solution of the Schrödinger Equation for q-deformed Attractive Radial Plus Coulomb-like Molecular Potential within the Framework of NU-Method

Arbitrary l-state Solution of the Schrödinger Equation for q-deformed Attractive Radial Plus Coulomb-like Molecular Potential within the Framework of NU-Method

Analytical approximate bound state solution of Schrödinger equation in D-dimensions with a new mixed class of potential for arbitrary ℓ-state via asymptotic iteration method

The bound state solutions of the D-dimensional Schrödinger equation for new mixed class of potential, V(r)=V1r2+V2e−αrr+V3cothαr+V4, are studied within the framework of the Pekeris approximation for any arbitrary ℓ-state. Asymptotic iteration method (AIM) is used for the work. The energy spectrum are obtained as well as their corresponding normalized eigenfunctions are derived in terms of generalized hypergeometric functions 2F1(a, b, c; z). It is shown that using the Pekeris approximation, present potential model is very much capable of deriving other well known potentials quite easily and corresponding solutions are in excellent agreement with the previous work carried out in the literature.

Analytical solutions of position-dependent mass Klein–Gordon equation for unequal scalar and vector Yukawa potentials

Analytical solutions of the position-dependent mass Klein–Gordon equation in the presence of unequal scalar and vector Yukawa potentials for arbitrary l-state are obtained by using the generalized parametric Nikiforov–Uvarov method. With an approximation scheme to deal with the centrifugal term, we get the bound state energy eigenvalues and the corresponding wave functions, expressed in terms of the Jacobi polynomials. Subsequently, we consider a special case for α = 0 and explicitly obtain the energy eigenvalues as well as the corresponding eigenfunctions in terms of the Laguerre polynomials. Some results are also compared with the previous studies.

Scattering State of Coupled Hulthen–Woods–Saxon Potentials for the Duffin–Kemmer–Petiau Equation with Pekeris Approximation for the Centrifugal Term

Abstract We studied the approximate analytical scattering state of the Duffin–Kemmer–Petiau (DKP) equation for arbitrary l-state for couple Hulthen–Woods–Saxon potential using the Pekeris approximation for the centrifugal term. We obtained an energy spectrum, normalised radial wave functions of the scattering states, and the corresponding formula for the phase shifts, which is derived in detail. Special cases of Hulthen and Woods–Saxon potentials were also studied.

Arbitrary ℓ-state solutions of the Feynman propagator with the Deng-Fan molecular potential

The bound state solutions of the Feynman propagator with the rotating Deng- Fan molecular potential are presented approximately. An approximation of the centrifugal potential is used and nonlinear space-time transformations are applied. A relation between the original path integral and the Green function of a new quantum soluble system is derived. The energy spectrum and the normalized eigenfunctions are both obtained for the application of this technique to the Deng-Fan molecular potential. Our results are in very good agreement with those found by using numerical and other methods.

Solutions of Nonrelativistic Schrödinger Equation with Scarf II Plus Rosen-Morse II Potential via Ansaltz Method

We have solved the non-relativistic Schrodinger equation with Scarf II plus Rosen-Morse II potential analytically for arbitrary l-state by using the newly improved ansaltz for the wave function and adopting the modified approximation scheme to evaluate the centrifugal term. The bound state energy spectrum and the un-normalized wave function expressed in terms of Jacobi polynomial are also obtained. With this method, we have obtained a negative energy spectrum for the system.

Solutions of D-dimensional Klein–Gordon equation for multiparameter exponential-type potential using supersymmtric quantum mechanics

In this paper, we present solutions of the Klein–Gordon equation for the multiparameter potential for arbitrary l-state in D-dimensions using the super-symmetric quantum mechanics method. We have obtained the energy levels for the multiparameter potential and the corresponding wave functions expressed in terms of hypergeometric function in a closed form for arbitrary l-state. We have discussed in detail the special cases of this potential.

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

We present the bound state solution of Schrödinger 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 closed form. We also compute the energy eigenvalues numerically.

Arbitrary l-state solutions of the Feynman propagator for the Rosen-Morse Potential with a centrifugal term approximation

We present analytic solutions of the Feynman propagator with the Rosen-Morse potential. To do that, an approximation of the centrifugal potential is used and nonlinear space-time transformations are applied. A relation between the original path integral and the Green function of a new quantum soluble system is derived. Explicit expressions of the bound state energy spectra and the eigenfunctions are obtained and compared to those of Schrodinger formalism.

Spinless Particles Subject to Unequal Scalar-Vector Nuclear Woods– Saxon Potentials in Arbitrary Dimensions

We present analytical bound state solutions of the spin-zero particles in the Klein-Gordon (KG) equation in presence of an unequal mixture of scalar and vector Woods-Saxon potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a parametric Nikiforov-Uvarov (NU) method. Our numerical energy eigenvalues demonstrate the existence of inter-dimensional degeneracy amongst energy states of the KG-Woods-Saxon problem. The dependence of the energy levels on the dimension D is numerically discussed for spatial dimensions D = 2 - 6.

Approximate Solution of the Spin-0 Particle Subject to the Trigonometric Pöschl–Teller Potential with Centrifugal Barrier

The trigonometric Pöschl-Teller (PT) potential describes the diatomic molecular vibration. In this paper, we study the approximate solutions of the radial Klein-Gordon (KG) equation for the rotating trigonometric PT potential using the Nikiforov-Uvarov (NU) method. The energy eigenvalues and their corresponding eigenfunctions are calculated for arbitrary l-states in closed form. We obtain the non-relativistic limit and present some numerical results for both relativistic and non-relativistic cases.

Solutions of the Second Pöschl–Teller Potential Solved by an Improved Scheme to the Centrifugal Term

Using an improved approximate formula to the centrifugal term, we present arbitrary l-state bound and scattering solutions of the second Poschl–Teller potential. We find that our approximate formula is better than a previous one since the calculated results are in better agreement with numerically exact ones.

Relativistic Treatment of Spinless Particles Subject to a q-Deformed Morse Potential

The approximate analytical solutions of the Klein—Gordon equation with equal scalar and vector q-deformed Morse potential are presented for arbitrary ℓ-states by using Laplace integral transform. The energy eigenvalues and corresponding wave functions are obtained for n and ℓ values. In this study, in the non-relativistic limit c → ∞, it has been also provided that the energy eigenfunctions for Klein—Gordon system turn into those for Schrödinger one.

A semi-relativistic treatment of spinless particles subject to the nuclear Woods-Saxon potential

By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter (SS) equation with the Woods-Saxon interaction potential for an arbitrary l-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied: the approximated Schrödinger-Woods-Saxon problem for an arbitrary l-state and the exact s-wave (l=0).