Rosen-Morse Type Research Articles

The complete solution of the Schrödinger equation with the Rosen–Morse type potential via the Nikiforov–Uvarov method

We determine exact solutions of the time-independent Schrödinger equation for the Rosen–Morse type potential by using the Nikiforov–Uvarov method. This method allows us to write the eigenfunctions of the Schrödinger equation as the product of two simpler functions in a constructive way. The resolution of this problem is used to show that the kinks of the non-linear Klein–Gordon equation with φ2p+2 type potentials are stable. We also derive the orthogonality and completeness relations satisfied by the set of eigenfunctions, which are useful in the description of the dynamics of kinks under perturbations or interacting with antikinks.

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 $$q\le -1$$ , and $$\frac{1}{2\alpha }\ln \left| q\right|<r<+\infty$$ , 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 for the bound state energy levels $$E_{n_{r}}$$ are transcendental equations which can be solved numerically. Three special cases such as the standard radial Manning–Rosen potential $$(\left| q\right| =1)$$ , the standard radial Rosen–Morse potential $$(V_{2}\rightarrow -V_{2},q=1)$$ and the radial Eckart potential $$(V_{1}\rightarrow -V_{1},q=1)$$ are also briefly discussed.

Rosen-Morse potentials for relativistic spinless particles; approximate solutions

We deal with the D-dimensional radial Klein-Gordon equation for Rosen-Morse type potential with unequal scalar and vector potentials. We apply a proper approximation to the centrifugal term and, by proposing an ansatz solution to the resulting equation, we obtain the bound-state solution. To check the accuracy of our results, we compare our obtained quasi-analytical energies with the exact numerical ones.

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 the standard Rosen–Morse well and Eckart potentials in the special case. The PT-symmetry for these potentials is also considered.

Simple unified derivation and solution of Coulomb, Eckart and Rosen-Morse potentials in prepotential approach

The four exactly solvable models related to non-sinusoidal coordinates, namely, the Coulomb, Eckart, Rosen-Morse type I and II models are normally being treated separately, despite the similarity of the functional forms of the potentials, their eigenvalues and eigenfunctions. Based on an extension of the prepotential approach to exactly and quasi-exactly solvable models proposed previously, we show how these models can be derived and solved in a simple and unified way.

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.

GENERALIZED BÄCKLUND–DARBOUX TRANSFORMATIONS IN ONE-DIMENSIONAL QUANTUM MECHANICS

We consider an action of the group of curves in GL(2,ℝ) on the set of linear systems and therefore on the set of Schrödinger equations in full similarity with the action of the group of curves in SL(2,ℝ) on the set of Riccati equations considered in previous articles. We also consider the transformations defined by a first-order differential expression which carry solutions of a Schrödinger equation into solutions of another one. We find then two non-trivial situations: transformations which can be described by the previous transformation group, generalizing previous work by us, and transformations which are singular. We show that both situations appear, e.g., in the usual problem of partner Hamiltonians in quantum mechanics. We show that the difference Bäcklund algorithm, both in the finite and confluent versions, can be understood in terms of the above mentioned transformation group, the case of two exactly equal factorization energies being an instance of the singular case. We apply the generalized theorem relating three eigenfunctions of three different Hamiltonians to the generation of new potentials with a known (excited state) eigenfunction, starting from potentials of Coulomb, Morse and Rosen–Morse type. The potentials found are new and non-trivial.

Simultaneous ordinary and type A [formula omitted] supersymmetries in Schrödinger, Pauli, and Dirac equations

We investigate physical models which possess simultaneous ordinary and type A N - fold supersymmetries, which we call type A ( N , 1 ) - fold supersymmetry. Inequivalent type A ( N , 1 ) - fold supersymmetric models with real-valued potentials are completely classified. Among them, we find that a trigonometric Rosen–Morse type and its elliptic version are of physical interest. We investigate various aspects of these models, namely, dynamical breaking and interrelation between ordinary and N - fold supersymmetries, shape invariance, quasi-solvability, and an associated algebra which is composed of one bosonic and four fermionic operators and dubbed type A ( N , 1 ) - fold superalgebra. As realistic physical applications, we demonstrate how these systems can be embedded into Pauli and Dirac equations in external electromagnetic fields.

Simultaneous type A [formula omitted]-fold supersymmetry with two different values of [formula omitted

We investigate one-dimensional quantum mechanical systems which have type A N -fold supersymmetry with two different values of N simultaneously. We find that there are essentially four inequivalent models possessing the property, one is conformal, two of them are hyperbolic (trigonometric) including Rosen–Morse type, and the other is elliptic.

Exact solutions of the Schrödinger equation with position-dependent mass for some Hermitian and non-Hermitian potentials

We study the exact solutions of the Schrödinger equation with position-dependent mass by using the method of point canonical transformations. Given a position-dependent mass distribution, we construct the exactly solvable target potentials by choosing the Rosen–Morse-type and Scarf-type potentials as the reference potentials. The energy spectra of the bound states and corresponding wavefunctions for the target potentials are given explicitly.

Bound states of the Klein–Gordon equation with vector and scalar Rosen–Morse-type potentials

Solving Klein–Gordon equation with equal scalar and vector Rosen–Morse-type potentials, we obtain the exact energy equation for the s-wave bound states. It has been shown that the energy equations and corresponding wavefunctions for the standard Rosen–Morse well, Eckart potential and their PT-symmetric versions are included in those for Rosen–Morse-type potential as special cases.

Nonradiative transitions in benzene

A symmetric Rosen-Morse potential was assumed for the potential of the out-of-plane vibrations of benzene. Matrix elements and the respectiveS1 ⇝S0 nonradiative rates were calculated for several values of the anharmonicity constants and compared with the results obtained with a harmonic potential. Anharmonicities of the out-of-plane modes in benzene are found to decrease the values of the matrix elements and rates, thus leaving unresolved, a discrepancy between experimental and theoreticalS1 ⇝S0 rates for benzene. However, in molecules with distorted acceptor modes whose frequencies are higher in the optically excited, as compared to the acceptor state, increases of several orders of magnitude of the nonradiative rate could occur on introduction of Rosen-Morse type anharmonicities.