Energy spectra of the hyperbolic and second Pöschl–Teller like potentials solved by new exact quantization rule

The extension of the quantization rule approach to non-central potentials is investigated. The energy spectra for the generalized Coulomb and oscillator systems are presented. The results are in good agreement with those obtained before.

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Approximate analytical solutions for arbitrary l-state of the Hulthén potential with an improved approximation of the centrifugal term

Open Chemistry ◽

10.2478/s11532-011-0050-6 ◽

2011 ◽

Vol 9 (4) ◽

pp. 737-742 ◽

Cited By ~ 8

Author(s):

Jerzy Stanek

Keyword(s):

Bound State ◽

Centrifugal Term ◽

Approximate Methods ◽

Quantization Rule ◽

Hulthén Potential ◽

Hulthen Potential ◽

Approximate Analytical Solutions ◽

Exact Quantization Rule ◽

Screening Parameter ◽

Uvarov Method

AbstractAn approximate analytical solution of the radial Schrödinger equation for the generalized Hulthén potential is obtained by applying an improved approximation of the centrifugal term. The bound state energy eigenvalues and the normalized eigenfunctions are given in terms of hypergeometric polynomials. The results for arbitrary quantum numbers n r and l with different values of the screening parameter δ are compared with those obtained by the numerical method, asymptotic iteration, the Nikiforov-Uvarov method, the exact quantization rule, and variational methods. The results obtained by the method proposed in this work are in a good agreement with those obtained by other approximate methods.

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Dirac particle in the external coulomb field on the background of the Lobachevsky–Riemann space models

Doklady of the National Academy of Sciences of Belarus ◽

10.29235/1561-8323-2021-65-2-146-157 ◽

2021 ◽

Vol 65 (2) ◽

pp. 146-157

Author(s):

E. M. Оvsiyuk ◽

A. D. Koral’kov

Keyword(s):

Hydrogen Atom ◽

Dirac Equation ◽

Differential Equations ◽

Exact Solutions ◽

Coulomb Field ◽

Dirac Particle ◽

Riemann Space ◽

Energy Spectra ◽

Spaces Of Constant Curvature ◽

Quantization Rule

The known systems of the radial equations describing the hydrogen atom on the basis of the Dirac equation in the Lobachevsky–Riemann spaces of constant curvature are investigated. In the both geometrical models, the differential equations of second order with six regular singular points are found, and their exact solutions of Frobenius type are constructed. To produce the quantization rule for energy values we use the known condition which separates the transcendental Frobenius solutions. This provides us with the energy spectra that are physically interpretable and are similar to those for the Klein–Fock–Gordon particle in these space models. These spectra are similar to those that previously have appeared in studying the same systems of the equations with the use of the semi-classical approximation.

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ROTATIONAL-VIBRATIONAL EIGEN SOLUTIONS OF THE D-DIMENSIONAL SCHRÖDINGER EQUATION FOR THE IMPROVED WEI POTENTIAL

FUDMA Journal of Sciences ◽

10.33003/fjs-2020-0402-174 ◽

2020 ◽

Vol 4 (2) ◽

pp. 269-283

Author(s):

Edwin Samson Eyube ◽

Yabwa Dlama ◽

Umar Wadata

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Goodness Of Fit ◽

Bound State ◽

Fit Indices ◽

Quantization Rule ◽

Exact Quantization Rule ◽

Vibrational Energies ◽

Eigen Solutions ◽

Tietz Potential

In this present study, we have employed the techniques of exact quantization rule and ansatz solution method to obtain closed form expressions for the rotational-vibrational eigensolutions of the D-dimensional Schrödinger equation for the improved Wei potential, for cases of h′ ≠ 0 and h′ = 0. By using our derived energy equation and choosing arbitrary values of n and ℓ, we have computed the bound state rotational-vibrational energies of CO, H2 and LiH for various quantum states. The mean absolute percentage deviation (MAPD) and the Lippincott criterion ware used as a goodness-of-fit indices to compare our result with the Rydberg-Klein-Rees (RKR) and improved Tietz potential data in the literature. MAPD of 0.2862%, 0.2896% and 0.0662% relative to the RKR data for CO ware obtained. For the improved Wei and Morse potential, our computed energy eigenvalues for CO, H2 and LiH are in excellent agreement with existing results in the literature

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EXACT QUANTIZATION RULE AND ITS APPLICATIONS TO PHYSICAL POTENTIALS

International Journal of Modern Physics E ◽

10.1142/s0218301307005661 ◽

2007 ◽

Vol 16 (01) ◽

pp. 189-198 ◽

Cited By ~ 53

Author(s):

SHI-HAI DONG ◽

D. MORALES ◽

J. GARCÍA-RAVELO

Keyword(s):

Harmonic Oscillator ◽

Analytical Solutions ◽

Bound States ◽

Energy Levels ◽

Present Approach ◽

Three Dimensions ◽

One Dimension ◽

Quantization Rule ◽

Exact Quantization Rule ◽

Pseudoharmonic Oscillator

By using the exact quantization rule, we present analytical solutions of the Schrödinger equation for the deformed harmonic oscillator in one dimension, the Kratzer potential and pseudoharmonic oscillator in three dimensions. The energy levels of all the bound states are easily calculated from this quantization rule. The normalized wavefunctions are also obtained. It is found that the present approach can simplify the calculations.

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