Poschl-Teller Research Articles

Coherent States and Modified de Broglie-Bohm Complex Quantum Trajectories

This paper examines the nature of classical correspondence in the case of coherent states at the level of quantum trajectories. We first show that for a harmonic oscillator, the coherent state complex quantum trajectories and the complex classical trajectories are identical to each other. This congruence in the complex plane, not restricted to high quantum numbers alone, illustrates that the harmonic oscillator in a coherent state executes classical motion. The quantum trajectories we consider are those conceived in a modified de Broglie-Bohm scheme. Though quantum trajectory representations are widely discussed in recent years, identical classical and quantum trajectories for coherent states are obtained only in the present approach. We may note that this result for standard harmonic oscillator coherent states is not totally unexpected because of their holomorphic nature. The study is extended to coherent states of a particle in an infinite potential well and that in a symmetric Poschl-Teller potential by solving for the trajectories numerically. For the Gazeau-Klauder coherent state of the infinite potential well, almost identical classical and quantum trajectories are obtained whereas for the Poschl-Teller potential, though classical trajectories are not regained, a periodic motion results as t→∞. Similar features were found for the SUSY quantum mechanics-based coherent states of the Poschl-Teller potential too, but this time the pattern of complex trajectories is quite different from that of the previous case. Thus we find that the method is a potential tool in analyzing the properties of generalized coherent states.

Approximate analytical solutions to relativistic and nonrelativistic Pöschl–Teller potential with its thermodynamic properties

We apply the asymptotic iteration method (AIM) to obtain the solutions of Schrödinger equation in the presence of Pöschl–Teller (PT) potential. We also obtain the solutions of Dirac equation for the same potential under the condition of spin and pseudospin (p-spin) symmetries. We show that in the nonrelativistic limits, the solution of Dirac system converges to that of Schrödinger system. Rotational and vibrational energy eigenvalues of some diatomic molecules are calculated. Some special cases of interest are studied such as S-wave case, reflectionless-type potential and symmetric hyperbolic PT potential. Furthermore, we present a high temperature partition function in order to study the behavior of the thermodynamic functions such as the vibrational mean energy U, specific heat C, free energy F and entropy S.

Bound and scattering states of spinless particles under the generalized Pöschl–Teller potential

Bound and scattering state solutions of Klein–Gordon equation are obtained for equal scalar and vector Generalized Poschl–Teller potentials with angular momentum l. Energy eigenvalues, normalized wave functions and scattering phase shifts are calculated.

Corrigendum: Energy spectrum for trigonometric Pöschl–Teller potential solved by the asymptotic iteration method.

Received 7 January 2013. Accepted 7 February 2013. B.J. Falaye. Theoretical Physics Section, Department of Physics University of Ilorin, P. M. B. 1515, Ilorin, Nigeria. E-mail for correspondence: fbjames11@physicist.net. Table 1. Bound state energies for the special case l = 0, obtained with parameters V1 = 5 fm–1, V2 = 3 fm–1, and = 10 fm–1. n AIM, = 0.2 NU, = 0.2 AIM, = 0.02 NU, = 0.02 AIM, = 0.002 NU, = 0.002 0 16.104 941 73 16.104 941 72 15.781 498 98 15.781 498 98 15.749 516 29 15.749 516 29 1 16.830 826 21 16.830 826 21 15.852 642 89 15.852 642 89 15.756 616 28 15.756 616 28 2 17.572 710 70 17.572 710 70 15.923 946 80 15.923 946 80 15.763 717 86 15.763 717 86 3 18.330 595 18 18.330 595 18 15.995 410 71 15.995 410 71 15.770 821 05 15.770 821 05 4 19.104 479 67 19.104 479 67 16.067 034 63 16.067 034 63 15.777 925 84 15.777 925 84 5 19.894 364 16 19.894 364 16 16.138 818 54 16.138 818 54 15.785 032 22 15.785 032 22 6 20.700 248 64 20.700 248 64 16.210 762 45 16.210 762 45 15.792 140 21 15.792 140 21 Note: All NU values are taken from ref. 2. 365

Exact Solution of Klein–Gordon Equation for Hua Plus Modified Eckart Potentials

We report the exact s-wave solutions of the Klein–Gordon equation under equal scalar and vector the Hua plus modified Eckart potentials using the functional analysis method. The results, in special cases, yield the results of Morse, Hua, Eckart and Poschl–Teller potentials.

The position–momentum uncertainty relations for a Pöschl–Teller type potential and its squeezed phenomena

Abstract We present the position–momentum uncertainties for the Poschl–Teller potential. We observe that the Δx decreases with the potential depth λ but increases with quantum number n. Interestingly, we find that the Δp first increases and then decreases with the n. The Δ x Δ p first decreases and then increases with the λ, but almost becomes a constant ( n + 1 / 2 ) ℏ for a larger λ. Particularly, there exists a squeezed phenomenon in position x for the lower states. The squeezing in x compensated for by an increase in momentum p, such that Δ x Δ p ⩾ ℏ / 2 is still satisfied.

Comments on the generalized SUSY QM partnership for Darboux–Pöschl–Teller potential and exceptional Jacobi polynomials

A recently proposed scheme to generate the rational extensions of translationally shape-invariant potentials is applied to the trigonometric Darboux–Poschl–Teller potential. It allows one in particular to obtain the two series of extensions \(J1\) and \(J2\) associated to the exceptional Jacobi polynomials. We give an explicit proof of the shape invariance of these extended potentials.

Spin and Pseudospin Symmetries with Trigonometric Pöschl-Teller Potential including Tensor Coupling

We study approximate analytical solutions of the Dirac equation with the trigonometric P&#xf6;schl-Teller (tPT) potential and a Coulomb-like tensor potential for arbitrary spin-orbit quantum number <i >&#x3ba;</i> under the presence of exact spin and pseudospin (<svg style="vertical-align:-3.50804pt;width:10.2px;" id="M1" height="13.3" version="1.1" viewBox="0 0 10.2 13.3" width="10.2" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.017,-0,0,-.017,.062,8.863)"><path id="x1D45D" d="M570 304q0 -108 -87 -199q-40 -42 -94.5 -74t-105.5 -43q-41 0 -65 11l-29 -141q-9 -45 -1.5 -58t45.5 -16l26 -2l-5 -29l-241 -10l4 26q51 10 67.5 24t26.5 60l113 520q-54 -20 -89 -41l-7 26q38 28 105 53l11 49q20 25 77 58l8 -7l-17 -77q39 14 102 14q82 0 119 -36&#xA;t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" /></g> </svg>-spin) symmetries. The bound state energy eigenvalues and the corresponding two-component wave functions of the Dirac particle are obtained using the parametric generalization of the Nikiforov-Uvarov (NU) method. We show that tensor interaction removes degeneracies between spin and pseudospin doublets. The case of nonrelativistic limit is studied too.

The Dirac equation with position-dependent mass for the modified Pschl-Teller potential and its solution

The Dirac-modified Poschl-Teller problem with position dependent mass is investigated within the framework of the asymptotic iteration method in N dimensions. Any -state solutions are obtained by using the exponential approximation for the centrifugal term. The energy eigenvalues and two-component spinor corresponding eigenfunctions are determined for different screening parameters explicitly. The corresponding eigenfunctions obtained in the form of hypergeometric functions are normalized and plotted for different quantum states. Effects on modified Poschl-Teller potential, bound state energy eigenvalues and normalized corresponding eigenfunctions of the screening parameters are investigated and its results are discussed. Key words: Dirac equation, position-dependent mass (PDM), Poschl-Teller (PT) potential, asymptotic iteration method, bound state.

Molecular bound and resonance state energies of the modified Pöschl–Teller like potential

The oscillator basis is used to tridiagonalize the reference Hamiltonian, and the Pöschl-Teller (PT) potential matrix elements have been calculated using the Gauss quadrature approach. The bound and resonance state energies of the modified Pöschl-Teller (MPT) potential are calculated using the J-matrix method, for states with arbitrary quantum numbers and . Comparisons are made with the available literature data and excellent agreement is observed. The calculation is also carried out for molecular systems. Furthermore, the average oscillator strength, multipole moments and transition probabilities for certain states have been reported for future comparison. Some new states close to the crossover region are reported for guiding future studies.

Electric field effect on the refractive index changes in a Modified-Pöschl-Teller quantum well

The effect of an applied static field is studied on the optical properties of a quantum well (QW) represented by a Modified Pöschl–Teller potential. This potential allows analytical solution of the eigen-values and eigen-functions which in turn makes the numerical calculation of optical properties quite transparent. In this work, we concentrate on the linear and nonlinear refractive index changes. Comparison of the results using the finite Modified-Pöschl–Teller (MPT) potential with those in the literature using the infinite Pöschl–Teller (PT) potential shows that the main difference between the two potentials is coming from the depth differences of the two wells. The changes in the refractive indices are bigger than those using infinite PT potential. If one wants a larger change in the total refractive index, one should try to reduce the applied electric fields and the optical intensities.

Approximate Dirac solutions of a complex parity–time-symmetric Pöschl–Teller potential in view of spin and pseudospin symmetries

By employing an exponential-type approximation scheme to replace the centrifugal term, we have approximately solved the Dirac equation for a spin-1/2 particle subjected to complex parity–time-symmetric scalar and vector Pöschl–Teller (PT) potentials with arbitrary spin–orbit -wave states in view of spin and pseudospin (p-spin) symmetries. The real bound-state energy eigenvalue equation and the corresponding two-spinor components wave function expressible in terms of hypergeometric functions are obtained by means of wave function analysis. The spin- Dirac equation and the spin-0 Klein–Gordon equation with complex PT potentials share the same energy spectrum under the choice of (i.e. exact spin and p-spin symmetries).

Approximate l-state solution of the trigonometric Pöschl–Teller potential

The trigonometric Pöschl–Teller (PT) potential describes diatomic molecular vibration. We have obtained the approximate solutions of the radial Schrödinger equation for the rotating trigonometric PT potential using the Nikiforov–Uvarov method. The energy eigenvalues and their corresponding eigenfunctions are calculated for arbitrary l-states in closed form. In the low-screening region, when the screening parameter the potential reduces to the Kratzer potential. Numerical results are presented for several diatomic molecules.

PSEUDOSPIN SYMMETRY IN TRIGONOMETRIC PÖSCHL–TELLER POTENTIAL

We investigated the analytical [Formula: see text]-wave solutions of Dirac equation for trigonometric Pöschl–Teller (PT) potential under the pseudospin symmetry condition. The energy eigenvalues equation and corresponding wave functions are obtained by using the Nikiforov–Uvarov (NU) method. The energy bound states are also calculated numerically.

Analysis of Energy Spectrum and Wave Function of Modified Poschl Teller Potential Using Hypergeometry and Supersymmetry Method

Modified Poschl Teller potential is a potential model used to describe behavior of inter moleculer forces. The spectrum energy and wave function of the particle affection in modified Poschl Teller potential are obtained by solving the Schrodinger equation, using hypergeometric equation and supersymmetric method. The energy spectrum and wave function are obtained from hypergeometric equation, which is constructed from Schrodinger equation through variable substitution. The energy spectrum and wave function are obtained using raising and lowering supersymmetric operator and applying shape invariance property. The solution of those equation of the energy spectrum and wave function obtained using these two methods are exact solution. Further, the wave function and density probability are visualized using computer simulation.

Approximate Solution of Schrodinger Equation for Trigonometric Scarf Potential with the Poschl-Teller Non-central potential Using NU Method

Abstract: The approximate analytical solution of Schrodinger equation for Scarf potential plus trigonometricPoschl-Teller potential is investigated using Nikiforov-Uvarov method. The bound state energy eigenvalues are given in the close form and the corresponding radial and angular eigenfunctions are formulated in the form of the generalized Jacobi Polynomials. The trigonometric Poschl-Teller potential causes the energy of Scarf potensial decreases as the orbital quantum number increases. The energy spectrum and the radial wave function of Scarf potential are produced by the absent of Poschl-Teller potential. Keywords: Nikiforov-Uvarov method, Schrodinger equation, Trigonometric Scarf I, Poschl-Teller potential.

Algebraic approach to energy spectra of the Scarf type and generalized Pöschl–Teller potentials

Using the shape invariance approach, we obtain analytical energy spectra of the Scarf-type and generalized Poschl–Teller potentials and calculate them numerically. The eigenfunctions are also presented for completeness. We find that their eigenfunctions can be expressed by the Nomanovski polynomials and hypergeometric functions, respectively. The key point is how to find their superpotentials using the Sturm–Liouville theorem.

Exact S‐wave solution of the trigonometric pöschl‐teller potential

AbstractThe trigonometric Pöschl‐Teller (PT) potential describes the diatomic molecular vibration. By using the Nikiforov‐Uvarov method, we have obtained the exact analytical s‐wave solutions of the radial Schrödinger equation (SE) for the trigonometric PT potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented too. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Solution of the Dirac Equation with Position-Dependent Mass for q-Parameter Modified Pöschl–Teller and Coulomb-like Tensor Potential

In this research, we have been obtained the Dirac equation for q-parameter modified Poschl–Teller potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number by choosing a position-dependent mass. The energy eigenvalues equation and the corresponding unnormalized wave functions have been obtained. The Nikiforov-Uvarov method has been used in the calculations.

Deformed photon-added nonlinear coherent states and their non-classical properties

In this paper, we will try to present a general formalism for the construction of deformed photon-added nonlinear coherent states (DPANCSs) |α, f, m⟩, which in a special case lead to the well-known photon-added coherent state (PACS) |α, m⟩. Some algebraic structures of the introduced DPANCSs are studied and particularly the resolution of the identity, as the most important property of generalized coherent states, is investigated. Meanwhile, it will be demonstrated that the introduced states can also be classified in the f-deformed coherent states, with a special nonlinearity function. Next, we will show that these states can be produced through a simple theoretical scheme. A discussion on the DPANCSs with negative values of m, i.e. |α, f, −m⟩, is then presented. Our approach has the potentiality to be used for the construction of a variety of new classes of DPANCSs, corresponding to any nonlinear oscillator with known nonlinearity function, as well as arbitrary solvable quantum system with known discrete, non-degenerate spectrum. Finally, after applying the formalism to a particular physical system known as the Pöschl–Teller (P-T) potential and the nonlinear coherent states corresponding to a specific nonlinearity function , some of the non-classical properties, such as the Mandel parameter, second-order correlation function, in addition to first- and second-order squeezing of the corresponding states, will be investigated numerically.